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 -