TY - RPRT TI - Numerical methods for adaptive-optics systems AU - Chu, Moody T. AU - Plemmons, R. DA - 1995/// PY - 1995/// M3 - Preprint ER - TY - RPRT TI - On the refinement of a Newton method for the inverse Toeplitz eigenvalue Problem AU - Chu, Moody DA - 1995/// PY - 1995/// M3 - Preprint ER - TY - RPRT TI - On a new geometric meaning of the BFGS update AU - Chu, Moody T. AU - Funderlic, R.E. AU - Golub, G.H. DA - 1995/// PY - 1995/// M3 - Preprint ER - TY - JOUR TI - A list of matrix flows with applications AU - Chu, Moody T2 - Hamiltonian and Gradient Flows, Algorithms and Control DA - 1995/5/2/ PY - 1995/5/2/ DO - 10.1090/fic/003/07 SP - 87-97 UR - http://dx.doi.org/10.1090/fic/003/07 ER - TY - JOUR TI - Constructing a Hermitian Matrix from Its Diagonal Entries and Eigenvalues AU - Chu, Moody T. T2 - SIAM Journal on Matrix Analysis and Applications AB - Given two vectors $a,\lambda \in R^n $, the Schur–Horn theorem states that a majorizes $\lambda $ if and only if there exists a Hermitian matrix H with eigenvalues $\lambda $ and diagonal entries a. While the theory is regarded as classical by now, the known proof is not constructive. To construct a Hermitian matrix from its diagonal entries and eigenvalues therefore becomes an interesting and challenging inverse eigenvalue problem. Two algorithms for determining the matrix numerically are proposed in this paper. The lift and projection method is an iterative method that involves an interesting application of the Wielandt–Hoffman theorem. The projected gradient method is a continuous method that, besides its easy implementation, offers a new proof of existence because of its global convergence property. DA - 1995/1// PY - 1995/1// DO - 10.1137/s0895479893243177 VL - 16 IS - 1 SP - 207-217 UR - http://dx.doi.org/10.1137/s0895479893243177 ER - TY - JOUR TI - The educational testing problem revisited AU - Chu, M.T. AU - Wright, J.W. T2 - IMA Journal of Numerical Analysis AB - Journal Article The educational testing problem revisited Get access MOODY T. CHU, MOODY T. CHU Department of Mathematics, North Carolina State UniversityRaleigh, North Carolina 27695-8205, USA Search for other works by this author on: Oxford Academic Google Scholar JOEL W. WRIGHT JOEL W. WRIGHT Department of Mathematics, North Carolina State UniversityRaleigh, North Carolina 27695-8205, USA Search for other works by this author on: Oxford Academic Google Scholar IMA Journal of Numerical Analysis, Volume 15, Issue 1, 1995, Pages 141–160, https://doi.org/10.1093/imanum/15.1.141 Published: 01 January 1995 Article history Received: 08 December 1992 Revision received: 10 May 1993 Published: 01 January 1995 DA - 1995/// PY - 1995/// DO - 10.1093/imanum/15.1.141 VL - 15 IS - 1 SP - 141-160 UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-21844482940&partnerID=MN8TOARS ER - TY - JOUR TI - Scaled Toda-like flows AU - Chu, M.T. T2 - Linear Algebra and Its Applications AB - This paper discusses the class of isospectral flows Ẋ = [X, A ∘ X], where ∘ denotes the Hadamard product and [., .] is the Lie bracket. The presence of A allows arbitrary and independent scaling for each element in the matrix X. The time-1 mapping of the scaled Toda-like flow still enjoys a QR-like iteration. The scaled structure includes the classical Toda flow, Brockett's double bracket flow, and other interesting flows as special cases. Convergence proof is thus unified and simplified. The effect of scaling on a variety of applications is demonstrated by examples. DA - 1995/// PY - 1995/// DO - 10.1016/0024-3795(93)00091-D VL - 215 IS - C SP - 261-273 UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-0040928421&partnerID=MN8TOARS ER - TY - JOUR TI - Rank-one reduction formula and its applications to matrix factorizations AU - Chu, Moody T. AU - Funderlic, Robert E. AU - Golub, Gene H. T2 - SIAM Review AB - Let $A \in R^{m \times n} $ denote an arbitrary matrix. If $x \in R^n $ and $y \in R^m $ are vectors such that $\omega = y^T Ax \ne 0$, then the matrix $B: = A - \omega ^{ - 1} Axy^T A$ A has rank exactly one less than the rank of A. This Wedderburn rank-one reduction formula is easy to prove, yet the idea is so powerful that perhaps all matrix factorizations can be derived from it. The formula also appears in places such as the positive definite secant updates BFGS and DFP as well as the ABS methods. By repeatedly applying the formula to reduce ranks, a biconjugation process analogous to the Gram–Schmidt process with oblique projections can be developed. This process provides a mechanism for constructing factorizations such as ${\text{LDM}}^T $, QR, and SVD under a common framework of a general biconjugate decomposition $V^T AU = \Omega $ that is diagonal and nonsingular. Two characterizations of biconjugation provide new insight into the Lanczos method and its breakdown. One characterization shows that the Lanczos algorithm (and the conjugate gradient method) is a special case of the rank-one process; in fact, these processes can be identified with the class of biconjugate direction methods so that history is pushed back by about twenty years. DA - 1995/// PY - 1995/// DO - 10.1137/1037124 VL - 37 IS - 4 SP - 512-530 UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-0029543087&partnerID=MN8TOARS ER - TY - CONF TI - Simulation of bubbles in creeping flow using the immersed interface method AU - LeVeque, R. J. AU - Li, Zhilin T2 - sixth international symposium on computational fluid dynamics C2 - 1995/// C3 - Proceedings of the sixth international symposium on computational fluid dynamics CY - Lake Tahoe DA - 1995/// PY - 1995/9/4/ SP - 688–693 ER - TY - CONF TI - The geometry of square invertible linear systems, matrix pencils, and predictive control AU - Campbell, Stephen L. AU - Delebecque, F. AU - Nikoukhah, R. AU - von Wissel, D. T2 - European Control Conference A2 - Isidori, A. A2 - Bittanti, S. A2 - Mosca, E. A2 - De Luca, A. A2 - Di Benedetto, M.D. A2 - Oriolo, G. C2 - 1995/// C3 - Proceedings of the third European Control Conference (ECC 95) CY - Rome, Italy DA - 1995/// PY - 1995/9/5/ SP - 2962–2967 ER - TY - CONF TI - Maneuver planning and robust path tracking for mobile robotic nonholonomic systems AU - Campbell, Stephen L. AU - Zhu, S.Q. AU - Lewis, F.L. AU - Ito, K. T2 - European Control Conference C2 - 1995/// C3 - Proceedings of the European Control Conference CY - Rome, Italy DA - 1995/// PY - 1995/9/5/ SP - 3080–3085 ER - TY - JOUR TI - Numerically Generated Path Stabilizing Controllers: Use of Preliminary Feedback AU - Campbell, Stephen L. AU - von Wissel, Dirk AU - Nikoukhah, Ramine AU - Delebecque, Francois T2 - Kybernetika DA - 1995/// PY - 1995/// VL - 31 IS - 6 SP - 657–668 ER - TY - JOUR TI - Modelling the spatial patterning of the teeth primordia in the lower jaw of Alligator mississippiensis AU - Kulesa, P. M. AU - Cruywagen, G. C. AU - Lubkin, S. R. AU - Maini, P. K. AU - Sneyd, J. AU - Murray, J. D. T2 - Journal of Biological Systems, Vol 3, Nos 1-4, 1995: Special Issue: 2nd Ecmbm-Lyon, Pts 1-4 DA - 1995/// PY - 1995/// SP - 975-985 UR - http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=ORCID&SrcApp=OrcidOrg&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=WOS:A1995BF06V00086&KeyUID=WOS:A1995BF06V00086 ER - TY - BOOK TI - A pair formation approach to modeling inheritance of social traits AU - Lubkin, S. AU - CastilloChavez, C. A3 - Lakshmikantham, V. DA - 1995/// PY - 1995/// PB - SE - 3227-3234 UR - http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=ORCID&SrcApp=OrcidOrg&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=WOS:A1995BF46J00295&KeyUID=WOS:A1995BF46J00295 ER - TY - JOUR TI - A MECHANISM FOR EARLY BRANCHING IN LUNG MORPHOGENESIS AU - Lubkin, S. R. AU - Murray, J. D. T2 - Journal of Mathematical Biology DA - 1995/// PY - 1995/// DO - 10.1007/bf00180137 VL - 34 IS - 1 SP - 77-94 UR - http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=ORCID&SrcApp=OrcidOrg&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=WOS:A1995TF94000004&KeyUID=WOS:A1995TF94000004 KW - LUNG KW - PATTERN FORMATION KW - MORPHOGENESIS KW - FETAL DEVELOPMENT ER - TY - CONF TI - On computing greatest common divisors with polynomials given by black boxes for their evaluations AU - Díaz, Angel AU - Kaltofen, Erich T2 - ISSAC95: International Symposium on Symbolic and Algebraic Computation A2 - Levelt, A.H.M. AB - Article On computing greatest common divisors with polynomials given by black boxes for their evaluations Share on Authors: Angel Díaz Department of Computer Science, Rensselaer Polytechnic Institute, Troy, New York Department of Computer Science, Rensselaer Polytechnic Institute, Troy, New YorkView Profile , Erich Kaltofen Department of Computer Science, Rensselaer Polytechnic Institute, Troy, New York Department of Computer Science, Rensselaer Polytechnic Institute, Troy, New YorkView Profile Authors Info & Claims ISSAC '95: Proceedings of the 1995 international symposium on Symbolic and algebraic computationApril 1995 Pages 232–239https://doi.org/10.1145/220346.220375Online:01 April 1995Publication History 11citation268DownloadsMetricsTotal Citations11Total Downloads268Last 12 Months3Last 6 weeks1 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my AlertsNew Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteGet Access C2 - 1995/// C3 - Proceedings of the 1995 international symposium on Symbolic and algebraic computation - ISSAC '95 CY - Montreal Quebec Canada DA - 1995/// PY - 1995/7/10/ DO - 10.1145/220346.220375 PB - ACM Press SN - 0897916999 9780897916998 UR - http://dx.doi.org/10.1145/220346.220375 ER - TY - JOUR TI - Traveling Wave Solutions of the Modified Korteweg-deVries-Burgers Equation AU - Jacobs, D. AU - Mckinney, B. AU - Shearer, M. T2 - Journal of Differential Equations DA - 1995/3// PY - 1995/3// DO - 10.1006/jdeq.1995.1043 VL - 116 IS - 2 SP - 448-467 J2 - Journal of Differential Equations LA - en OP - SN - 0022-0396 UR - http://dx.doi.org/10.1006/jdeq.1995.1043 DB - Crossref ER - TY - CHAP TI - Mathematical Issues in Optimal Design of a Vapor Transport Reactor AU - Ito, K. AU - Tran, H.T. AU - Scroggs, J.S. T2 - Flow Control A2 - Gunzburger, Max D. T3 - The IMA Volumes in Mathematics and its Applications AB - In this paper the optimal design of a vertical reactor for growing crystals and epitaxial layers by physical vapor transport technique is discussed. The transport phenomena involved in the deposition process is modeled by the gasdynamics equations and chemical kinematics. The problem is formulated as a shape optimization with respect to the geometry of the reactor and an optimal control problem by controlling the wall temperature. The material and shape derivatives of solutions to the so-called Boussinesq approximation are derived. Optimality condition and a numerical optimization method based on the augmented Lagrangian method are discussed for the boundary control of the Boussinesq flow. A numerical approximation based on the Jacobi polynomials for the axi-symmetric flow is developed along with a discussion of an iterative method based on GMRES for solving the resulting system of nonlinear equations. PY - 1995/// DO - 10.1007/978-1-4612-2526-3_9 SP - 197–218 PB - Springer SN - 9781461275695, 9781461225263 SV - 68 ER - TY - CONF TI - Human Respiratory Control System and Periodic Breathing AU - Batzel, J.J. AU - Tran, H.T. T2 - 32nd Annual Technical Meeting of the Society of Engineering Science C2 - 1995/// C3 - SES' 95 : Society of Engineering Science 32nd annual technical meeting, October 29 - November 2, 1995, New Orleans, LA CY - New Orleans, LA DA - 1995/// PY - 1995/10/29/ SP - 623–624 ER - TY - CONF TI - High Pressure Vapor Transport of ZnGeP 2 : II, Three-Dimensional Simulation of Gas-dynamics under Microgravity Conditions AU - Scroggs, J.S. AU - Banks, H.T. AU - Ito, K. AU - Ravindran, S. AU - Tran, H.T. AU - Bachmann, K.J. AU - Castleberry, R.H. AU - Dietz, N. T2 - Annual Meeting of TMS A2 - Schiffman, R. C2 - 1995/// C3 - 7th International Symposium on Experimental Methods for Microgravity Materials Science : proceedings of the Seventh International Conference on Experimental Methods for Microgravity Materials Science CY - Las Vegas, NV DA - 1995/// PY - 1994/2/12/ SP - 67–72 PB - Minerals, Metals and Materials Society, ER - TY - CONF TI - High Pressure Vapor Transport of ZnGeP 2 : I, Parameter Evaluation AU - Fiechter, S. AU - Castleberry, R.H. AU - Dietz, N. AU - Bachmann, K.J. AU - Banks, H.T. AU - Ito, K. AU - Scroggs, J.S. AU - Tran, H. T2 - Annual Meeting of TMS A2 - Schiffman, R.A. C2 - 1995/// C3 - 7th International Symposium on Experimental Methods for Microgravity Materials Science : proceedings of the Seventh International Conference on Experimental Methods for Microgravity Materials Science CY - Las Vegas, NV DA - 1995/// PY - 1994/2/12/ SP - 57–66 PB - Minerals, Metals and Materials Society, ER - TY - CONF TI - Implicitization of Curves Parameterized by Generalized Trigonometric Polynomials AU - Hong, Hoon A2 - Cohen, Gérard D. A2 - Giusti, Marc A2 - Mora, Teo C2 - 1995/// C3 - Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, 11th International Symposium, AAECC-11, Paris, France, July 17-22, 1995, Proceedings DA - 1995/// DO - 10.1007/3-540-60114-7\_21 VL - 948 SP - 285-296 PB - Springer UR - https://doi.org/10.1007/3-540-60114-7\_21 ER - TY - JOUR TI - The Design of the SACLIB/PACLIB Kernels AU - Hong, Hoon AU - Neubacher, Andreas AU - Schreiner, Wolfgang T2 - Journal of Symbolic Computation AB - This paper describes the design of the runtime systems of two variants of the SAC-2 computer algebra library: SACLIB and PACLIB. SACLIB is a C version of SAC-2, supporting automatic garbage collection and embeddability. PACLIB is a parallel version of SACLIB, supporting light-weight concurrency, non-determinism, virtual tasks, and parallel garbage collection. DA - 1995/1// PY - 1995/1// DO - 10.1006/jsco.1995.1007 VL - 19 IS - 1-3 SP - 111-132 UR - http://dx.doi.org/10.1006/jsco.1995.1007 ER - TY - JOUR TI - Preface AU - Hong, Hoon AU - Wang, Dongming AU - Winkler, Franz T2 - Annals of Mathematics and Artificial Intelligence DA - 1995/3// PY - 1995/3// DO - 10.1007/bf01531320 VL - 13 IS - 1-2 SP - I-II UR - http://dx.doi.org/10.1007/bf01531320 ER - TY - JOUR TI - Bernstein form is inclusion monotone AU - Hong, H. AU - Stahl, V. T2 - Computing DA - 1995/3// PY - 1995/3// DO - 10.1007/bf02238236 VL - 55 IS - 1 SP - 43-53 UR - http://dx.doi.org/10.1007/bf02238236 KW - INTERVAL ANALYSIS KW - RANGE COMPUTATION KW - INCLUSION MONOTONICITY KW - BERNSTEIN COEFFICIENTS ER - TY - JOUR TI - Fully nonlinear hyperbolic systems of partial differential equations related to plasticity AU - Shearer, Michael AU - Schaeffer, David G. T2 - Communications in Partial Differential Equations AB - In this paper, we study systems of two fully nonlinear partial differential equations in one space dimension, of the form U{sub t}+F(U{sub x})+O, where U=U(x,t){element_of}{Re}{sup 2}. The nonlinearity F : {Re}{sup 2}{r_arrow} {Re}{sup 2} is homogeneous of degree one, i.e. F({alpha}V)={alpha}F(V), for all {alpha}>O, and is smooth away from the origin. A model example is provided by F(V)+AV+b{vert_bar}V{vert_bar}, where A is a 2x2 matrix and b{var_epsilon}{Re}, which was studied. 4 refs., 5 figs. DA - 1995/1// PY - 1995/1// DO - 10.1080/03605309508821127 VL - 20 IS - 7-8 SP - 1133-1153 J2 - Communications in Partial Differential Equations LA - en OP - SN - 0360-5302 1532-4133 UR - http://dx.doi.org/10.1080/03605309508821127 DB - Crossref ER - TY - JOUR TI - The Riemann problem for a system of conservation laws of mixed type with a cubic nonlinearity AU - Shearer, Michael AU - Yang, Yadong T2 - Proceedings of the Royal Society of Edinburgh: Section A Mathematics AB - Using the viscosity-capillarity admissibility criterion for shock waves, we solve the Riemann problem for the system of conservation laws where σ( u ) = u 3 − u . This system is hyperbolic at ( u , v ) unless . We find that the Riemann problem has a unique solution for all data in the hyperbolic regions, except for a range of data in the same phase (i.e. on the same side of the nonhyperbolic strip). In the nonunique cases, there are exactly two admissible solutions. The analysis is based upon a formula describing all saddle-to-saddle heteroclinic orbits for a family of cubic vector fields in the plane. DA - 1995/// PY - 1995/// DO - 10.1017/s0308210500030298 VL - 125 IS - 4 SP - 675-699 J2 - Proceedings of the Royal Society of Edinburgh: Section A Mathematics LA - en OP - SN - 0308-2105 1473-7124 UR - http://dx.doi.org/10.1017/s0308210500030298 DB - Crossref ER - TY - CHAP TI - Restauration ensembliste d’images par itérations parallèles extrapolées de sous-gradients AU - Combettes, P.L. T2 - Actes du Quinzième Colloque GRETSI PY - 1995/9/18/ SP - 447–450 UR - http://hdl.handle.net/2042/12207 ER - TY - CONF TI - Adaptive linear filtering with convex constraints AU - Combettes, P.L. AU - Bondon, P. T2 - 1995 International Conference on Acoustics, Speech, and Signal Processing AB - We address the problem of linear mean-square estimation with arbitrary convex constraints for dependent processes. Two algorithms are proposed and their convergence is established. The first algorithm, which is deterministic, covers the case of known correlation structures; the second, which is stochastic and adaptive, covers the case of unknown correlation structures. Since existing algorithms can handle at most one simple constraint this contribution is relevant to signal processing problems in which arbitrary convex inequality constraints are present. C2 - 1995/5/8/ C3 - 1995 International Conference on Acoustics, Speech, and Signal Processing CY - Detroit, Michigan DA - 1995/5/8/ PY - 1995/5/9/ DO - 10.1109/icassp.1995.480496 VL - 2 SP - 1372–1375 PB - IEEE SN - 0780324315 UR - http://dx.doi.org/10.1109/icassp.1995.480496 ER - TY - CONF TI - Constrained image recovery in a product space AU - Combettes, P.L. T2 - International Conference on Image Processing AB - In image recovery a priori knowledge and the observed data give rise to constraints on the solutions. In general, the recovery problem can be posed as that of minimizing a pertinent cost function over the resulting feasibility set. In this paper we present a product space framework for solving such problems, which leads to simplified formulations and to efficient parallel algorithms. Feasibility problems, quadratic minimization problems, and convex minimization problems are discussed. C2 - 1995/11/19/ C3 - Proceedings., International Conference on Image Processing CY - Washington, DC DA - 1995/11/19/ PY - 1995/10/23/ DO - 10.1109/icip.1995.537406 VL - 2 SP - 25–28 PB - IEEE Comput. Soc. Press SN - 0780331222 UR - http://dx.doi.org/10.1109/icip.1995.537406 ER - TY - JOUR TI - A class of fully nonlinear 2×2 systems of partial differential equations AU - Shearer, Michael AU - Schaeffer, David G. T2 - Communications in Partial Differential Equations AB - This paper is a study of certain fully nonlinear 2×2 systems of partial differential equations in one space variable and time. The nonlinearity contains a term proportional to |∂U/∂x| where U = U(x,t) $isinv; ℝ2 is the unknown function and |·| is the Euclidean norm on ℝ2; i.e., a term homogeneous of degree 1 in ∂U/∂x and singular at the origin. Such equations are motivated by hypoplasticity. The paper introduces a notion of hyperbolicity for such equations and, in the hyperbolic case, proves existence of solutions for two initial value problems admitting similarity solutions: the Riemann problem and the scale-invariant problem. Uniqueness is addressed in a companion paper. DA - 1995/1// PY - 1995/1// DO - 10.1080/03605309508821126 VL - 20 IS - 7-8 SP - 1105-1131 J2 - Communications in Partial Differential Equations LA - en OP - SN - 0360-5302 1532-4133 UR - http://dx.doi.org/10.1080/03605309508821126 DB - Crossref ER - TY - JOUR TI - Linearization of DAEs along trajectories AU - Campbell, Stephen L. T2 - ZAMP Zeitschrift f�r angewandte Mathematik und Physik DA - 1995/1// PY - 1995/1// DO - 10.1007/bf00952257 VL - 46 IS - 1 SP - 70-84 J2 - Z. angew. Math. Phys. LA - en OP - SN - 0044-2275 1420-9039 UR - http://dx.doi.org/10.1007/bf00952257 DB - Crossref ER - TY - JOUR TI - Constraint preserving integrators for general nonlinear higher index DAEs AU - Campbell, Stephen L. AU - Moore, Edward T2 - Numerische Mathematik DA - 1995/2/1/ PY - 1995/2/1/ DO - 10.1007/s002110050099 VL - 69 IS - 4 SP - 383-399 J2 - Numerische Mathematik OP - SN - 0029-599X 0945-3245 UR - http://dx.doi.org/10.1007/s002110050099 DB - Crossref ER - TY - JOUR TI - Solvability of General Differential Algebraic Equations AU - Campbell, Stephen L. AU - Griepentrog, E. T2 - SIAM Journal on Scientific Computing AB - In the last few years there has been considerable research on differential algebraic equations (DAEs) $f(t,x,x') = 0$ where $f_{x'} $ is identically singular. Most of this effort has focused on computing a solution that is assumed to exist. That is, the DAE is assumed solvable. More recently there have been existence results developed using differential geometry. For complex higher index systems these characterizations can be hard to verify in practice. In this paper the computational verification of solvability is investigated. This first requires developing an alternative set of sufficient conditions for solvability which are more amenable to computation. Verification of these conditions using readily available numerical and symbolic software is then discussed. An example from robotics where classical graph theoretical approaches give an incorrect answer is worked to illustrate the usefulness of the sufficient condition and the computational approach. DA - 1995/3// PY - 1995/3// DO - 10.1137/0916017 VL - 16 IS - 2 SP - 257-270 J2 - SIAM J. Sci. Comput. LA - en OP - SN - 1064-8275 1095-7197 UR - http://dx.doi.org/10.1137/0916017 DB - Crossref KW - LEAST SQUARES KW - DIFFERENTIAL ALGEBRAIC EQUATIONS KW - SOLVABILITY KW - COMPLETIONS KW - NUMERICAL METHODS ER - TY - JOUR TI - Nonregular 2D descriptor delay systems AU - Campbell, Stephen L. T2 - IMA Journal of Mathematical Control and Information AB - This paper examines descriptor systems with delays which are in the form Bx′(t) + Dx(t) + Cx(t − α) = Eu(t) . Previous paper have examined the case when λB + D is a regular pencil. In this paper we examine the case when λ B + D is a singular pencil but det(λ B + D + ω C )≢0. Behaviour not previously reported for descriptor systems is observed. Several basic issues are discussed. DA - 1995/// PY - 1995/// DO - 10.1093/imamci/12.1.57 VL - 12 IS - 1 SP - 57-67 J2 - IMA J Math Control Info LA - en OP - SN - 0265-0754 1471-6887 UR - http://dx.doi.org/10.1093/imamci/12.1.57 DB - Crossref ER - TY - JOUR TI - Analysis of Coppersmith’s block Wiedemann algorithm for the parallel solution of sparse linear systems AU - Kaltofen, Erich T2 - Mathematics of Computation AB - By using projections by a block of vectors in place of a single vector it is possible to parallelize the outer loop of iterative methods for solving sparse linear systems. We analyze such a scheme proposed by Coppersmith for Wiedemann’s coordinate recurrence algorithm, which is based in part on the Krylov subspace approach. We prove that by use of certain randomizations on the input system the parallel speed up is roughly by the number of vectors in the blocks when using as many processors. Our analysis is valid for fields of entries that have sufficiently large cardinality. Our analysis also deals with an arising subproblem of solving a singular block Toeplitz system by use of the theory of Toeplitz-like matrices. DA - 1995/5/1/ PY - 1995/5/1/ DO - 10.1090/s0025-5718-1995-1270621-1 VL - 64 IS - 210 SP - 777-777 J2 - Math. Comp. LA - en OP - SN - 0025-5718 UR - http://dx.doi.org/10.1090/s0025-5718-1995-1270621-1 DB - Crossref ER - TY - JOUR TI - Integer division in residue number systems AU - Hitz, M.A. AU - Kaltofen, E. T2 - IEEE Transactions on Computers AB - This contribution to the ongoing discussion of division algorithm for residue number systems (RNS) is based on Newton iteration for computing the reciprocal. An extended RNS with twice the number of moduli provides the range required for multiplication and scaling. Separation of the algorithm description from its RNS implementation achieves a high level of modularity, and makes the complexity analysis more transparent. The number of iterations needed is logarithmic in the size of the quotient for a fixed start value. With preconditioning it becomes the logarithm of the input bit size. An implementation of the conversion to mixed radix representation is outlined in the appendix.< > DA - 1995/// PY - 1995/// DO - 10.1109/12.403714 VL - 44 IS - 8 SP - 983-989 J2 - IEEE Trans. Comput. OP - SN - 0018-9340 UR - http://dx.doi.org/10.1109/12.403714 DB - Crossref KW - INTEGER DIVISION KW - RECIPROCAL KW - NEWTON ITERATION KW - EXTENDED RESIDUE NUMBER SYSTEM KW - MIXED RADIX CONVERSION KW - BASE EXTENSION ER - TY - JOUR TI - Process Scheduling in DSC and the Large Sparse Linear Systems Challenge AU - Dı́az, A. AU - Hitz, M. AU - Kaltofen, E. AU - Lobo, A. AU - Valente, T. T2 - Journal of Symbolic Computation AB - New features of our DSC system for distributing a symbolic computation task over a network of processors are described. A new scheduler sends parallel subtasks to those compute nodes that are best suited in handling the added load of CPU usage and memory. Furthermore, a subtask can communicate back to the process that spawned it by a co-routine style calling mechanism. Two large experiments are described in this improved setting. In the first we have implemented an algorithm that can prove a number of more than 1,000 decimal digits prime in about 2 months elapsed time on some 20 computers. In the second a parallel version of a sparse linear system solver is used to compute the solution of sparse linear systems over finite fields. We are able to find the solution of a 100,000 by 100,000 linear system with about 10.3 million non-zero entries over the Galois field with 2 elements using 3 computers in about 54 hours CPU time. DA - 1995/1// PY - 1995/1// DO - 10.1006/jsco.1995.1015 VL - 19 IS - 1-3 SP - 269-282 J2 - Journal of Symbolic Computation LA - en OP - SN - 0747-7171 UR - http://dx.doi.org/10.1006/jsco.1995.1015 DB - Crossref ER - TY - JOUR TI - Effective Noether Irreducibility Forms and Applications AU - Kaltofen, E. T2 - Journal of Computer and System Sciences AB - Using recent absolute irreducibility testing algorithms, we derive new irreducibility forms. These are integer polynomials in variables which are the generic coefficients of a multivariate polynomial of a given degree. A (multivariate) polynomial over a specific field is said to be absolutely irreducible if it is irreducible over the algebraic closure of its coefficient field. A specific polynomial of a certain degree is absolutely irreducible, if and only if all the corresponding irreducibility forms vanish when evaluated at the coefficients of the specific polynomial. Our forms have much smaller degrees and coefficients than the forms derived originally by Emmy Noether. We can also apply our estimates to derive more effective versions of irreducibility theorems by Ostrowski and Deuring and of the Hilbert irreducibility theorem. We also give an effective estimate on the diameter of the neighborhood of an absolutely irreducible polynomial with respect to the coefficient space in which absolute irreducibility is preserved. Furthermore, we can apply the effective estimates to derive several factorization results in parallel computational complexity theory: we show how to compute arbitrary high precision approximations of the complex factors of a multivariate integral polynomial and how to count the number of absolutely irreducible factors of a multivariate polynomial with coefficients in a rational function field, both in the complexity class NC. The factorization results also extend to the case where the coefficient field is a function field. DA - 1995/4// PY - 1995/4// DO - 10.1006/jcss.1995.1023 VL - 50 IS - 2 SP - 274-295 J2 - Journal of Computer and System Sciences LA - en OP - SN - 0022-0000 UR - http://dx.doi.org/10.1006/jcss.1995.1023 DB - Crossref ER - TY - JOUR TI - Strong Convergence of the Empirical Distribution of Eigenvalues of Large Dimensional Random Matrices AU - Silverstein, J.W. T2 - Journal of Multivariate Analysis AB - Let X be n × N containing i.i.d. complex entries with E |X11 − EX11|2 = 1, and T an n × n random Hermitian nonnegative definite, independent of X. Assume, almost surely, as n → ∞, the empirical distribution function (e.d.f.) of the eigenvalues of T converges in distribution, and the ratio n/N tends to a positive number. Then it is shown that, almost surely, the e.d.f. of the eigenvalues of (1/N) XX*T converges in distribution. The limit is nonrandom and is characterized in terms of its Stieltjes transform, which satisfies a certain equation. DA - 1995/11// PY - 1995/11// DO - 10.1006/jmva.1995.1083 VL - 55 IS - 2 SP - 331-339 J2 - Journal of Multivariate Analysis LA - en OP - SN - 0047-259X UR - http://dx.doi.org/10.1006/jmva.1995.1083 DB - Crossref KW - random matrix KW - empirical distribution function of eigenvalues KW - Stieltjes transform ER - TY - JOUR TI - Analysis of the Limiting Spectral Distribution of Large Dimensional Random Matrices AU - Silverstein, J.W. AU - Choi, S.I. T2 - Journal of Multivariate Analysis AB - Results on the analytic behavior of the limiting spectral distribution of matrices of sample covariance type, studied in Marcenko and Pastur [2] and Yin [8], are derived. Through an equation defining its Stieltjes transform, it is shown that the limiting distribution has a continuous derivative away from zero, the derivative being analytic wherever it is positive, and resembles [formula] for most cases of x0 in the boundary of its support. A complete analysis of a way to determine its support, originally outlined in Marčenko and Pastur [2], is also presented. DA - 1995/8// PY - 1995/8// DO - 10.1006/jmva.1995.1058 VL - 54 IS - 2 SP - 295-309 J2 - Journal of Multivariate Analysis LA - en OP - SN - 0047-259X UR - http://dx.doi.org/10.1006/jmva.1995.1058 DB - Crossref KW - EIGENVALUES OF RANDOM MATRICES KW - SPECTRAL DISTRIBUTION KW - STIELTJES TRANSFORM ER - TY - JOUR TI - On the Empirical Distribution of Eigenvalues of a Class of Large Dimensional Random Matrices AU - Silverstein, J.W. AU - Bai, Z.D. T2 - Journal of Multivariate Analysis AB - A stronger result on the limiting distribution of the eigenvalues of random Hermitian matrices of the form A + XTX*, originally studied in Marčenko and Pastur, is presented. Here, X(N × n), T(n × n), and A(N × N) are independent, with X containing i.i.d. entries having finite second moments, T is diagonal with real (diagonal) entries, A is Hermitian, and n/N → c > 0 as N → ∞. Under additional assumptions on the eigenvalues of A and T, almost sure convergence of the empirical distribution function of the eigenvalues of A + XTX* is proven with the aid of Stieltjes transforms, taking a more direct approach than previous methods. DA - 1995/8// PY - 1995/8// DO - 10.1006/jmva.1995.1051 VL - 54 IS - 2 SP - 175-192 J2 - Journal of Multivariate Analysis LA - en OP - SN - 0047-259X UR - http://dx.doi.org/10.1006/jmva.1995.1051 DB - Crossref KW - RANDOM MATRIX KW - EMPIRICAL DISTRIBUTION FUNCTION OF EIGENVALUES KW - STIELTJES TRANSFORM ER - TY - JOUR TI - Vertex operators of quantum affine Lie algebras Uq(Dn (1)) AU - Jing, N. AU - Kang, S.-J. AU - Koyama, Y. T2 - Communications in Mathematical Physics AB - We give an explicit formula for the vertex operators related to the level 1 representations of the quantum affine Lie algebrasU q (D (1) ) in terms of bosons. As an application, we derive an integral formula for the correlation functions of the vertex models withU q (D (1) )-symmetry. DA - 1995/// PY - 1995/// DO - 10.1007/BF02099607 VL - 174 IS - 2 SP - 367-392 UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-0000124645&partnerID=MN8TOARS ER - TY - JOUR TI - Boson-fermion correspondence for Hall-Littlewood polynomials AU - Jing, N. T2 - Journal of Mathematical Physics DA - 1995/// PY - 1995/// VL - 36 IS - 12 SP - 7073-7080 UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-21844499602&partnerID=MN8TOARS ER - TY - CHAP TI - Optimal Control of Thermally Coupled Navier Stokes Equations AU - Ito, Kazufumi AU - Scroggs, Jeffrey S. AU - Tran, Hien T. T2 - Optimal Design and Control AB - The optimal boundary temperature control of the stationary thermally coupled incompressible Navier- Stokes equation is considered. Well-posedness and existence of the optimal control and a necessary optimality condition are obtained. Optimization algorithms based on the augmented Lagrangian method with second order update are discussed. A test example motivated by control of transport process in the high pressure vapor transport (HPVT) reactor is presented to demonstrate the applicability of our theoretical results and proposed algorithm. PY - 1995/// DO - 10.1007/978-1-4612-0839-6_13 SP - 199-214 OP - PB - Birkhäuser Boston SN - 9781461269168 9781461208396 UR - http://dx.doi.org/10.1007/978-1-4612-0839-6_13 DB - Crossref ER - TY - JOUR TI - Construction d'un point fixe commun à une famille de contractions fermes AU - Combettes, P.L. T2 - Comptes Rendus de l'Académie des Sciences de Paris, Série I (Mathématique) DA - 1995/6// PY - 1995/6// VL - 320 IS - 11 SP - 1385–1390 ER - TY - CONF TI - Nonlocal Artificial Boundary Conditions Based on the Difference Potentials Method AU - Tsynkov, S. V. A2 - Hafez, M. C2 - 1995/// C3 - Sixth International Symposium on Computational Fluid Dynamics. Collection of Technical Papers CY - Lake Tahoe, Nevada DA - 1995/// VL - IV SP - 114-119 UR - https://www.tib.eu/en/search/id/TIBKAT%3A228255147/A-collection-of-technical-papers-Sixth-International/ ER - TY - CHAP TI - Nonlocal Artificial Boundary Conditions for Computation of External Viscous Flows AU - Tsynkov, Semyon V. T2 - Computational Mechanics ’95 A2 - Atluri, S. N. A2 - Yagawa, G. A2 - Cruse, T. A. PY - 1995/// DO - 10.1007/978-3-642-79654-8_174 SP - 1065-1070 OP - PB - Springer Berlin Heidelberg SN - 9783642796562 9783642796548 UR - http://dx.doi.org/10.1007/978-3-642-79654-8_174 DB - Crossref ER - TY - JOUR TI - Deconvolution with bounded uncertainty AU - Combettes, Patrick L. AU - Trussell, H. Joel T2 - International Journal of Adaptive Control and Signal Processing AB - Abstract In deconvolution problems there are two primary sources of uncertainty in the data formation mechanism, namely measurement noise and errors in the model of the system. In this paper we develop an abstract set theoretic deconvolution framework for problems in which the only information available about these sources of uncertainty consists of bounds. Iterative methods based on projections are used to generate solutions consistent with these bounds, the output data signal and a priori knowledge about the input signal. an example of application of this general framework to discrete signal recovery is demonstrated. DA - 1995/1// PY - 1995/1// DO - 10.1002/acs.4480090103 VL - 9 IS - 1 SP - 3-17 J2 - Int. J. Adapt. Control Signal Process. LA - en OP - SN - 0890-6327 1099-1115 UR - http://dx.doi.org/10.1002/acs.4480090103 DB - Crossref KW - SIGNAL DECONVOLUTION KW - BOUNDED-ERROR KW - SET THEORETIC ESTIMATION KW - CONVEX SETS KW - PROJECTIONS ER - TY - JOUR TI - Volterra filtering and higher order whiteness AU - Bondon, P. AU - Combettes, P.L. AU - Picinbono, B. T2 - IEEE Transactions on Signal Processing AB - Some properties of Volterra filtering are established. Finite-order, finite-horizon Volterra filtering is investigated as well as its asymptotic properties. Next, the concepts of Volterra unpredictability and uninterpolability lead to generalizations of the notion of white noise to higher orders. These generalizations are introduced and relations are established between them.< > DA - 1995/// PY - 1995/// DO - 10.1109/78.414788 VL - 43 IS - 9 SP - 2209-2212 J2 - IEEE Trans. Signal Process. OP - SN - 1053-587X UR - http://dx.doi.org/10.1109/78.414788 DB - Crossref ER - TY - CONF TI - Implicit Filtering and Optimal Design Problems: Proceedings of the Workshop on Optimal Design and Control, {B}lacksburg {VA}, {A}pril 8--9, 1994 AU - Gilmore, P AU - Kelley, C T AU - Miller, C T AU - Williams, G A A2 - Borggaard, J A2 - Burkhardt, J A2 - Gunzburger, M A2 - Peterson, J C2 - 1995/// C3 - Optimal Design and Control DA - 1995/// VL - 19 SP - 159-176 PB - Birkh{ä}user, Boston ER - TY - BOOK TI - Iterative Methods for Linear and Nonlinear Equations AU - Kelley, C T DA - 1995/// PY - 1995/// PB - SIAM ER - TY - JOUR TI - Indentation of a thin compressible elastic layer: Approximate analytic and numerical solutions for rigid flat indenters AU - Haider, M.A. AU - Holmes, M.H. T2 - Journal of the Mechanics and Physics of Solids AB - Abstract Indentation of a thin compressible linearly elastic layer in bonded or frictionless contact with a rigid foundation is considered. Using the small parameter e = h a , an asymptotic analysis of the deformation for thin layers in plane strain is conducted. For flat indenters, the existence of an outer solution and interior layers near the edges of the indenter are demonstrated. In the interior layers, an analytic approximation is developed and closed form expressions for the vertical deformation and normal stress are obtained. The equilibrium equations and all but one (frictionless case) or two (bonded case) of the boundary conditions are satisfied. The approximation incorporates a large portion of the singular deformation gradients near the edge of the indenter and is in close agreement with known asymptotic results. A numerical study of the plane strain case shows that incorporation of the approximation into a numerical scheme greatly increases convergence rate, in that accurate results may be obtained on coarse meshes. DA - 1995/8// PY - 1995/8// DO - 10.1016/0022-5096(95)00032-e VL - 43 IS - 8 SP - 1199-1219 SN - 0022-5096 UR - http://dx.doi.org/10.1016/0022-5096(95)00032-e ER - TY - JOUR TI - The index of general nonlinear DAEs AU - Campbell, Stephen L. AU - Gear, C. William T2 - Numerische Mathematik DA - 1995/12/1/ PY - 1995/12/1/ DO - 10.1007/s002110050165 VL - 72 IS - 2 SP - 173-196 J2 - Numerische Mathematik OP - SN - 0029-599X 0945-3245 UR - http://dx.doi.org/10.1007/s002110050165 DB - Crossref ER - TY - JOUR TI - High-Index Differential Algebraic Equations AU - Campbell, Stephen L T2 - Mechanics of Structures and Machines AB - ABSTRACT In the last few years there has been considerable research on differential algebraic equations (DAEs) f(x1, x, t) = 0, where fx 1 is identically singular. The index provides one measure of the singularity of a DAE. Most of the numerical analysis literature on DAEs to date has dealt with DAEs with indices no larger than three, because of technical difficulties and because many basic applications including constrained mechanical systems have this index. This paper discusses several situations where DAEs of index higher than three occur naturally. It will also discuss the relationship between certain concepts in nonlinear control theory such as relative degree and zero dynamics, the index, and constrained mechanical systems. DA - 1995/1// PY - 1995/1// DO - 10.1080/08905459508905235 VL - 23 IS - 2 SP - 199-222 J2 - Mechanics of Structures and Machines LA - en OP - SN - 0890-5452 UR - http://dx.doi.org/10.1080/08905459508905235 DB - Crossref ER - TY - JOUR TI - Computing Bouts of the Prisoner's Dilemma AU - Lloyd, Alun L. T2 - Scientific American DA - 1995/6// PY - 1995/6// DO - 10.1038/scientificamerican0695-110 VL - 272 IS - 6 SP - 110-115 J2 - Sci Am OP - SN - 0036-8733 UR - http://dx.doi.org/10.1038/scientificamerican0695-110 DB - Crossref ER - TY - JOUR TI - Chaos : Its significance and detection in biology AU - Lloyd, A.L. AU - Lloyd, D. T2 - Biological Rhythm Research AB - Abstract Chaos is a mechanism which can generate random‐looking time series from simple deterministic systems. We outline the idea of deterministic chaos and discuss some biological examples where chaos is believed to play a part. The benefits that biological systems may gain from exhibiting chaotic dynamics are discussed. Establishing whether a system exhibits chaotic dynamics by examining a time series consisting of observations of a single variable is not an easy task. Several sophisticated techniques are examined, including dimensional analysis, estimation of Lyapunov exponents and nonlinear forecasting. There are many difficulties in applying these techniques; often the data requirements are large and noise in the data can give misleading results. We discuss the method of surrogate data, which can help avoid fallacious results. DA - 1995/5// PY - 1995/5// DO - 10.1080/09291019509360338 VL - 26 IS - 2 SP - 233-252 J2 - Biological Rhythm Research LA - en OP - SN - 0929-1016 1744-4179 UR - http://dx.doi.org/10.1080/09291019509360338 DB - Crossref KW - CHAOS KW - DETERMINISTIC SYSTEMS KW - NOISE KW - STOCHASTIC PROCESSES KW - APERIODIC KW - QUASI-PERIODIC KW - ARRYTHMIC KW - CIRCADIAN KW - TIME SERIES ANALYSIS ER - TY - JOUR TI - The coupled logistic map: a simple model for the effects of spatial heterogeneity on population dynamics AU - Lloyd, Alun L. T2 - Journal of Theoretical Biology AB - A simple model consisting of two diffusively coupled logistic maps is used to examine the effects of spatial heterogeneity on population dynamics. Examining the dynamic behaviour of the model using numerical methods, a wide range of behaviours are observed. It is shown that the coupling can stabilize individually chaotic populations, and that under different circumstances the coupling can cause individually stable periodic populations to undergo more complex behaviour. The system exhibits multiple attractors when the qualitative dynamics of the system depend on the initial conditions. Sudden changes in the structure of the attractors are seen for small changes in the parameters; these changes are known as crises. Transient and intermittent behaviours are observed. The implications of all these behaviours for populations are discussed. A linear coupling of the two maps is also considered which leads to counterintuitive behaviour, with chaotic dynamics being obtained by coupling two stable maps. This behaviour occurs because the coupling involves mixing of generations, and is therefore biologically unrealistic. DA - 1995/4// PY - 1995/4// DO - 10.1006/jtbi.1995.0058 VL - 173 IS - 3 SP - 217-230 J2 - Journal of Theoretical Biology LA - en OP - SN - 0022-5193 UR - http://dx.doi.org/10.1006/jtbi.1995.0058 DB - Crossref ER - TY - JOUR TI - Inexact primal-dual interior point iteration for linear programs in function spaces AU - Ito, S. AU - Kelley, C. T. AU - Sachs, E. W. T2 - Computational Optimization and Applications DA - 1995/7// PY - 1995/7// DO - 10.1007/bf01300870 VL - 4 IS - 3 SP - 189-201 J2 - Comput Optim Applic LA - en OP - SN - 0926-6003 1573-2894 UR - http://dx.doi.org/10.1007/bf01300870 DB - Crossref ER - TY - JOUR TI - On the Sensitivity of Solution Components in Linear Systems of Equations AU - Chandrasekaran, S. AU - Ipsen, I. C. F. T2 - SIAM Journal on Matrix Analysis and Applications AB - Expressions are presented for the errors in individual components of the solution to systems of linear equations and linear least squares problems. No assumptions about the structure or distribution of the perturbations are made. The resulting “componentwise condition numbers” measure the sensitivity of each solution component to perturbations. It is shown that any linear system has at least one solution component whose sensitivity to perturbations is proportional to the condition number of the matrix; but there may exist many components that are much better conditioned. Unless the perturbations are restricted, no norm-based relative error bound can predict the presence of well-conditioned components, so these componentwise condition numbers are essential. For the class of componentwise perturbations, necessary and sufficient conditions are given under which Skeel’s condition numbers are informative, and it is shown that these conditions are similar to conditions where componentwise condition numbers are useful. Numerical experiments not only confirm that these circumstances do occur frequently, they also illustrate that for many classes of matrices the ill conditioning of the matrix is due to a few rows of the inverse only. This means that many of the solution components are computed more accurately than current analyses predict. DA - 1995/1// PY - 1995/1// DO - 10.1137/s0895479892231255 VL - 16 IS - 1 SP - 93-112 J2 - SIAM J. Matrix Anal. & Appl. LA - en OP - SN - 0895-4798 1095-7162 UR - http://dx.doi.org/10.1137/s0895479892231255 DB - Crossref KW - CONDITION NUMBER KW - DIAGONAL SCALING KW - FORWARD ERROR KW - LINEAR SYSTEM KW - LEAST SQUARES KW - PERTURBATION THEORY ER - TY - JOUR TI - Analysis of a QR Algorithm for Computing Singular Values AU - Chandrasekaran, S. AU - Ipsen, I. C. F. T2 - SIAM Journal on Matrix Analysis and Applications AB - We extend the Golub–Kahan algorithm for computing the singular value decomposition of bidiagonal matrices to triangular matrices R. Our algorithm avoids the explicit formation of $R^T R$ or $RR^T$. We derive a relation between left and right singular vectors of triangular matrices and use it to prove monotonic convergence of singular values and singular vectors. The convergence rate for singular values equals the square of the convergence rate for singular vectors. The convergence behaviour explains the occurrence of deflation in the interior of the matrix. We analyse the relationship between our algorithm and rank-revealing QR and URV decompositions. As a consequence, we obtain an algorithm for computing the URV decomposition, as well as a divide-and-conquer algorithm that computes singular values of dense matrices and may be beneficial on a parallel architecture. Our perturbation result for the smallest singular values of a triangular matrix is stronger than the traditional results because it guarantees high relative accuracy in the smallest singular values after an off -diagonal block of the matrix has been set to zero. DA - 1995/4// PY - 1995/4// DO - 10.1137/s0895479892236532 VL - 16 IS - 2 SP - 520-535 J2 - SIAM J. Matrix Anal. & Appl. LA - en OP - SN - 0895-4798 1095-7162 UR - http://dx.doi.org/10.1137/s0895479892236532 DB - Crossref KW - SINGULAR VALUE DECOMPOSITION KW - EIGENVALUE DECOMPOSITION KW - QR DECOMPOSITION KW - RANK REVEALING QR DECOMPOSITION KW - URV DECOMPOSITION KW - DEFLATION ER - TY - JOUR TI - Relative Perturbation Techniques for Singular Value Problems AU - Eisenstat, Stanley C. AU - Ipsen, Ilse C. F. T2 - SIAM Journal on Numerical Analysis AB - A technique is presented for deriving bounds on the relative change in the singular values of a real matrix (or the eigenvalues of a real symmetric matrix) due to a perturbation, as well as bounds on the angles between the unperturbed and perturbed singular vectors (or eigenvectors). The class of perturbations considered consists of all $\delta B$ for which $B + \delta B = D_L BD_R $ for some nonsingular matrices $D_L $ and $D_R $. This class includes componentwise relative perturbations of a bidiagonal or biacyclic matrix and perturbations that annihilate the off-diagonal block in a block triangular matrix. Many existing relative perturbation and deflation bounds are derived from results for this general class of perturbations. Also some new relative perturbation and deflation results for the singular values and vectors of biacyclic, triangular, and shifted triangular matrices are presented. DA - 1995/12// PY - 1995/12// DO - 10.1137/0732088 VL - 32 IS - 6 SP - 1972-1988 J2 - SIAM J. Numer. Anal. LA - en OP - SN - 0036-1429 1095-7170 UR - http://dx.doi.org/10.1137/0732088 DB - Crossref KW - SINGULAR VALUE DECOMPOSITION KW - COMPONENTWISE RELATIVE PERTURBATIONS KW - DEFLATION CRITERIA KW - BIDIAGONAL MATRICES KW - BIACYCLIC MATRICES ER - TY - JOUR TI - The Angle Between Complementary Subspaces AU - Ipsen, Ilse C. F. AU - Meyer, Carl D. T2 - The American Mathematical Monthly DA - 1995/12// PY - 1995/12// DO - 10.1080/00029890.1995.12004683 VL - 102 IS - 10 SP - 904-911 J2 - The American Mathematical Monthly LA - en OP - SN - 0002-9890 1930-0972 UR - http://dx.doi.org/10.1080/00029890.1995.12004683 DB - Crossref ER - TY - JOUR TI - Solution of Optimal Control Problems by a Pointwise Projected Newton Method AU - Kelley, C. T. AU - Sachs, E. W. T2 - SIAM Journal on Control and Optimization AB - In the context of optimal control of ordinary differential equations, we prove local superlinear convergence and constraint identification results for an extension of the projected Newton method of Bertsekas. The estimates are also valid for discretized versions of the method-problem pair DA - 1995/11// PY - 1995/11// DO - 10.1137/s0363012993249900 VL - 33 IS - 6 SP - 1731-1757 J2 - SIAM J. Control Optim. LA - en OP - SN - 0363-0129 1095-7138 UR - http://dx.doi.org/10.1137/s0363012993249900 DB - Crossref KW - PROJECTED NEWTON ITERATION KW - OPTIMAL CONTROL ER - TY - JOUR TI - An Implicit Filtering Algorithm for Optimization of Functions with Many Local Minima AU - Gilmore, P. AU - Kelley, C. T. T2 - SIAM Journal on Optimization AB - In this paper we describe and analyze an algorithm for certain box constrained optimization problems that may have several local minima. A paradigm for these problems is one in which the function to be minimized is the sum of a simple function, such as a convex quadratic, and high frequency, low amplitude terms that cause local minima away from the global minimum of the simple function. Our method is gradient based and therefore the performance can be improved by use of quasi-Newton methods. DA - 1995/5// PY - 1995/5// DO - 10.1137/0805015 VL - 5 IS - 2 SP - 269-285 J2 - SIAM J. Optim. LA - en OP - SN - 1052-6234 1095-7189 UR - http://dx.doi.org/10.1137/0805015 DB - Crossref KW - FILTERING KW - PROJECTED GRADIENT ALGORITHM KW - QUASI-NEWTON METHOD ER - TY - JOUR TI - A Fast Multilevel Algorithm for Integral Equations AU - Kelley, C. T. T2 - SIAM Journal on Numerical Analysis AB - We show how the discretization of integral equations by composite Gauss rules can be related to approximations of integral operators that converge in the operator norm, rather than strongly converge. From this norm convergent formulation a two-level approximate inverse can be constructed whose evaluation requires no fine mesh evaluations of the integral operator. The resulting multilevel algorithm, therefore, is roughly half as costly as the Atkinson–Brakhage iteration. The algorithm is applicable to both linear and nonlinear equations. DA - 1995/4// PY - 1995/4// DO - 10.1137/0732021 VL - 32 IS - 2 SP - 501-513 J2 - SIAM J. Numer. Anal. LA - en OP - SN - 0036-1429 1095-7170 UR - http://dx.doi.org/10.1137/0732021 DB - Crossref KW - INTEGRAL EQUATIONS KW - MULTILEVEL METHODS KW - ATKINSON-BRAKHAGE ITERATION KW - COMPOSITE GAUSS RULE ER - TY - JOUR TI - Multilevel source iteration accelerators for the linear transport equation in slab geometry AU - Kelley, C. T. T2 - Transport Theory and Statistical Physics AB - Abstract In this paper we show how classical error estimates for various discretizations of the source iteration map in slab geometry can be used to construct accurate approximate inverses in the context of fast multilevel methods. For discretizations that give strongly convergent collectively compact sequences of approximate source iteration maps, the Atkinson-Brakhage approximate inverse can be applied. For discretizations that give rise to norm convergent sequences, a more direct approach can be used. Our implementation of these ideas, based on use of GMRES iteration to solve the coarse mesh problems, gives the solution to an accuracy of fine mesh truncation error at a cost proportional to that of an evaluation of the fine mesh source iteration map. These methods require only the source iteration map and are hence easier to adapt to multiprocessor computers than methods that require solution of diffusion equations. We illustrate our results with a report on numerical experiments with both strongly and norm convergent source iteration maps using the Kendall Square KSR1 computer. DA - 1995/4// PY - 1995/4// DO - 10.1080/00411459508206021 VL - 24 IS - 4-5 SP - 679-707 J2 - Transport Theory and Statistical Physics LA - en OP - SN - 0041-1450 1532-2424 UR - http://dx.doi.org/10.1080/00411459508206021 DB - Crossref ER - TY - JOUR TI - Well-Posedness of a Model for Structural Acoustic Coupling in a Cavity Enclosed by a Thin Cylindrical Shell AU - Banks, H.T. AU - Smith, R.C. T2 - Journal of Mathematical Analysis and Applications AB - A fully coupled mathematical model describing the interactions between a vibrating thin cylindrical shell and an enclosed acoustic field is presented. Because the model will ultimately be used in control applications involving piezoceramic actuators, the loads and material contributions resulting from piezoceramic patches bonded to the shell are included in the discussion. Theoretical and computational issues lead to the consideration of a weak form of the modeling set of partial differential equations (PDEs) and through the use of a semigroup formulation, well-posedness results for the system model are obtained. DA - 1995/4/1/ PY - 1995/4/1/ DO - 10.1016/s0022-247x(85)71117-1 VL - 191 IS - 1 SP - 1-25 SN - 0022-247X UR - http://dx.doi.org/10.1016/s0022-247x(85)71117-1 ER - TY - JOUR TI - The modeling of piezoceramic patch interactions with shells, plates, and beams AU - Banks, H. T. AU - Smith, R. C. AU - Wang, Yun T2 - Quarterly of Applied Mathematics AB - General models describing the interactions between one or a pair of piezoceramic patches and elastic substructures consisting of a cylindrical shell, plate, or beam are presented. In each case, the contributions to the internal moments and forces due to the presence of the patches are carefully discussed. In addition to these material contributions, the input of voltage to the patches produces mechanical strains that lead to external moments and forces. These external loads depend on the material properties of the patch, the geometry of patch placement, and the voltage. The internal and external moments and forces due to the patches are then incorporated into the equations of motion, which yields models describing the dynamics of the combined structure. These models are sufficiently general to allow for potentially different patch voltages, which implies that they can be suitably employed when using piezoceramic patches for controlling system dynamics when both extensional and bending vibrations are present. DA - 1995/6/1/ PY - 1995/6/1/ DO - 10.1090/qam/1330657 VL - 53 IS - 2 SP - 353-381 J2 - Quart. Appl. Math. LA - en OP - SN - 0033-569X 1552-4485 UR - http://dx.doi.org/10.1090/qam/1330657 DB - Crossref ER - TY - CHAP TI - Active Control of Acoustic Pressure Fields Using Smart Material Technologies AU - Banks, H. T. AU - Smith, R. C. T2 - Flow Control AB - An overview describing the use of piezoceramic patches in reducing noise in a structural acoustics setting is presented. The passive and active contributions due to patches which are bonded to an Euler-Bernoulli beam or thin shell are briefly discussed and the results are incorporated into a 2-D structural acoustics model. In this model, an exterior noise source causes structural vibrations which in turn lead to interior noise as a result of nonlinear fluid/structure coupling mechanisms. Interior sound pressure levels. are reduced via patches bonded to the flexible boundary (a beam in this case) which generate pure bending moments when an out-of-phase voltage is applied. Wellposedness results for the infinite dimensional system are discussed and a Galerkin scheme for approximating the system dynamics is outlined. Control is implemented by using LQR optimal control theory to calculate gains for the linearized system and then feeding these gains back into the nonlinear system of interest. The effectiveness of this strategy for this problem is illustrated in an example. PY - 1995/// DO - 10.1007/978-1-4612-2526-3_1 SP - 1-33 OP - PB - Springer New York SN - 9781461275695 9781461225263 UR - http://dx.doi.org/10.1007/978-1-4612-2526-3_1 DB - Crossref ER - TY - JOUR TI - An effective numerical technique for solving a special class of ordinary difference equations AU - Ryaben'kii, V.S. AU - Tsynkov, S.V. T2 - Applied Numerical Mathematics AB - We consider a system of ordinary difference equations with constant coefficients, which is defined on an infinite one-dimensional mesh. The right-hand side (RHS) of the system is compactly supported, therefore, the system appears to be homogeneous outside some finite mesh interval. At infinity, we impose certain boundary conditions, e.g., conditions of boundedness or decay of the solution, so that the resulting boundary-value problem is uniquely solvable and well posed. We also consider a truncation of this infinite-domain problem to some finite mesh interval that entirely contains the support of the RHS. We require that the solution to this truncated problem, which is the one we are going to actually calculate, coincides on the finite mesh interval where it is defined with the corresponding fragment of the solution to the original (infinite) problem. This requirement necessitates setting some special boundary conditions at the ends of the aforementioned finite interval. In so doing, one should guarantee an exact transfer of boundary conditions from infinity through the (semi-infinite) intervals of homogeneity of the original system. It turns out that the desired boundary conditions at the ends of the finite interval can be naturally formulated in terms of the eigen subspaces of the system operator. This, in turn, enables us to develop an effective numerical algorithm for solving the system of ordinary difference equations on the finite mesh interval. This algorithm can be referred to as a version of the well-known successive substitution technique but without its final (“inverse” or “resolving”) stage. The special class of systems described in this paper appears to be most useful when constructing highly accurate artificial boundary conditions (ABCs) for the numerical treatment of problems initially formulated on unbounded domains. Therefore, an effective numerical algorithm for solving such systems becomes an important issue. DA - 1995/10// PY - 1995/10// DO - 10.1016/0168-9274(95)00081-5 VL - 18 IS - 4 SP - 489-501 J2 - Applied Numerical Mathematics LA - en OP - SN - 0168-9274 UR - http://dx.doi.org/10.1016/0168-9274(95)00081-5 DB - Crossref ER - TY - JOUR TI - An Application of Nonlocal External Conditions to Viscous Flow Computations AU - Tsynkov, S.V. T2 - Journal of Computational Physics AB - We are looking for a steady-state solution of an external flow problem originally formulated on an unbounded domain. Our case is a 2D viscous compressible flow past a finite body (airfoil). We truncate the original domain by introducing a finite grid around the airfoil and integrate the Navier-Stokes equations on this grid with the help of a finite-volume code which involves a multigrid pseudo-time iteration technique for achieving a steady state. To integrate the Navier—Stokes equations on a finite subregion of an original domain only we supplement the numerical algorithm by special nonlocal artificial boundary conditions formulated on an external boundary of the finite computational domain. These artificial boundary conditions are based on the difference potentials method proposed by V. S. Ryaben'kii. We compare the results provided by the nonlocal conditions with those obtained from the standard external conditions which are based on locally one-dimensional characteristic analysis at inflow and extrapolation at outflow. It turns out that the nonlocal artificial boundary conditions accelerate the convergence by about a factor of 3, as well as allow one to shrink substantially the computational domain without loss of accuracy. DA - 1995/2// PY - 1995/2// DO - 10.1006/jcph.1995.1022 VL - 116 IS - 2 SP - 212-225 J2 - Journal of Computational Physics LA - en OP - SN - 0021-9991 UR - http://dx.doi.org/10.1006/jcph.1995.1022 DB - Crossref ER - TY - JOUR TI - Artificial Boundary Conditions for the Numerical Solution of External Viscous Flow Problems AU - Ryaben’kii, V. S. AU - Tsynkov, S. V. T2 - SIAM Journal on Numerical Analysis AB - In this paper we describe an algorithm for the nonlocal artificial boundary conditions setting at the external boundary of a computational domain while numerically solving unbounded viscous compressible flow problems past the finite bodies. Our technique is based on the usage of generalized Calderon projection operators and the application of the difference potentials method. Some computational results are presented. DA - 1995/10// PY - 1995/10// DO - 10.1137/0732063 VL - 32 IS - 5 SP - 1355-1389 J2 - SIAM J. Numer. Anal. LA - en OP - SN - 0036-1429 1095-7170 UR - http://dx.doi.org/10.1137/0732063 DB - Crossref KW - ARTIFICIAL BOUNDARY CONDITIONS KW - BOUNDARY EQUATIONS WITH PROJECTIONS KW - AUXILIARY PROBLEM KW - DIFFERENCE POTENTIALS METHOD ER -