TY - CONF
TI - Size efficient parallel algebraic circuits for partial derivatives
AU - Kaltofen, E.
AU - Singer, M.F.
A2 - Shirkov, D.V.
A2 - Rostovtsev, V.A.
A2 - Gerdt, V.P.
C2 - 1991///
C3 - IV International Conference on Computer Algebra in Physical Research
DA - 1991///
SP - 133–145
PB - World Scientific Publishing Co.
ER -
TY - CONF
TI - Least squares completions for nonlinear index three Hessenberg DAEs
AU - Campbell, Stephen L.
T2 - International Association for Mathematics and Computers in Simulation World Congress on Computation and Applied Mathematics
C2 - 1991///
C3 - IMACS '91 : proceedings of the 13th IMACS World Congress on Computation and Applied Mathematics : July 22-26, 1991, Trinity College, Dublin, Ireland
CY - Dublin, Ireland
DA - 1991///
PY - 1991/7/22/
SP - 1145–1148
PB - Criterion
ER -
TY - CONF
TI - 2-D (differential-delay) implicit systems
AU - Campbell, Stephen L.
T2 - International Association for Mathematics and Computers in Simulation World Congress on Computation and Applied Mathematics
C2 - 1991///
C3 - IMACS '91 : proceedings of the 13th IMACS World Congress on Computation and Applied Mathematics : July 22-26, 1991, Trinity College, Dublin, Ireland
CY - Dublin, Ireland
DA - 1991///
PY - 1991/7/22/
SP - 1828–1829
PB - Criterion Press
ER -
TY - JOUR
TI - ANALYTICAL MODEL OF CORNEAL SURGERY
AU - Rand, R. H.
AU - Lubkin, S. R.
AU - Howland, H. C.
T2 - Journal of Biomechanical Engineering-Transactions of the Asme
AB - We present a model of the human cornea in order to study the changes in its shape resulting from surgical operations (e.g., radial keratotomy). A simple closed-form solution is given for a thin linearly elastic spherical shell model of the cornea. We assume axisymmetry and isotropy in the shell surface. The surgery is modeled by permitting Young’s modulus and shell thickness to depend on position. The analytical nature of the solution permits principal shell curvatures to be explicitly calculated. The model is used to in vestigate the effect of surgery on corneal flattening and the associated sensitivity to intraocular pressure changes.
DA - 1991///
PY - 1991///
DO - 10.1115/1.2891240
VL - 113
IS - 2
SP - 239-241
UR - http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=ORCID&SrcApp=OrcidOrg&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=WOS:A1991HP74900018&KeyUID=WOS:A1991HP74900018
ER -
TY - CONF
TI - DSC: a system for distributed symbolic computation
AU - Diaz, A.
AU - Kaltofen, E.
AU - Schmitz, K.
AU - Valente, T.
T2 - ISSAC 91: International Symposium on Symbolic Algebraic Computation
A2 - Watt, S.M.
AB - Article Free AccessDSC: a system for distributed symbolic computation Share on Authors: A. Diaz Department of Computer Science, Rensselaer Polytechnic Institute, Troy, New York Department of Computer Science, Rensselaer Polytechnic Institute, Troy, New YorkView Profile , E. Kaltofen Department of Computer Science, Rensselaer Polytechnic Institute, Troy, New York Department of Computer Science, Rensselaer Polytechnic Institute, Troy, New YorkView Profile , K. Schmitz Department of Computer Science, Rensselaer Polytechnic Institute, Troy, New York Department of Computer Science, Rensselaer Polytechnic Institute, Troy, New YorkView Profile , T. Valente 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 '91: Proceedings of the 1991 international symposium on Symbolic and algebraic computationJune 1991 Pages 323–332https://doi.org/10.1145/120694.120772Online:01 June 1991Publication History 13citation168DownloadsMetricsTotal Citations13Total Downloads168Last 12 Months5Last 6 weeks3 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 SiteeReaderPDF
C2 - 1991///
C3 - Proceedings of the 1991 international symposium on Symbolic and algebraic computation - ISSAC '91
CY - Bonn, West Germany
DA - 1991///
PY - 1991/7/15/
DO - 10.1145/120694.120772
SP - 323-332
PB - ACM Press
SN - 0897914376 9780897914376
UR - http://dx.doi.org/10.1145/120694.120772
ER -
TY - CHAP
TI - On wiedemann's method of solving sparse linear systems
AU - Kaltofen, Erich
AU - Saunders, B. David
T2 - Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
A2 - Mattson, H.F.
A2 - Mora, T.
A2 - Rao, T.R.N.
T3 - Lecture Notes in Computer Science
PY - 1991///
DO - 10.1007/3-540-54522-0_93
SP - 29–38
PB - Springer
SN - 9783540545224 9783540384366
SV - 539
UR - http://dx.doi.org/10.1007/3-540-54522-0_93
ER -
TY - CHAP
TI - Explicit Construction of the Hilbert Class Fields of Imaginary Quadratic Fields by Integer Lattice Reduction
AU - Kaltofen, Erich
AU - Yui, Noriko
T2 - Number Theory
A2 - Chudnovsky, D.V.
A2 - Chudnovsky, G.V.
A2 - Cohn, H.
A2 - Nathanson, M.B.
PY - 1991///
DO - 10.1007/978-1-4757-4158-2_8
SP - 149–202
PB - Springer
SN - 9780387976709 9781475741582
UR - http://dx.doi.org/10.1007/978-1-4757-4158-2_8
ER -
TY - JOUR
TI - Undercompressive shocks for nonstrictly hyperbolic conservation laws
AU - Schecter, Stephen
AU - Shearer, Michael
T2 - Journal of Dynamics and Differential Equations
AB - We study 2×2 systems of hyperbolic conservation laws near an umbilic point. These systems have Undercompressive shock wave solutions, i.e., solutions whose viscous profiles are represented by saddle connections in an associated family of planar vector fields. Previous studies near umbilic points have assumed that the flux function is a quadratic polynomial, in which case saddle connections lie on invariant lines. We drop this assumption and study saddle connections using Golubitsky-Schaeffer equilibrium bifurcation theory and the Melnikov integral, which detects the breaking of heteroclinic orbits. The resulting information is used to construct solutions of Riemann problems.
DA - 1991/4//
PY - 1991/4//
DO - 10.1007/bf01047709
VL - 3
IS - 2
SP - 199-271
J2 - J Dyn Diff Equat
LA - en
OP -
SN - 1040-7294 1572-9222
UR - http://dx.doi.org/10.1007/bf01047709
DB - Crossref
ER -
TY - CHAP
TI - Numerical Studies of the Linear Quadratic Control Problem for Retarded Systems with Delay in Control
AU - Tran, Hien T.
T2 - Computation and Control II
AB - In this paper we report on the results of our continuing efforts on using the averaging approximation scheme for retarded functional differential equations. The central focus of this paper is our numerical studies of constructing feedback soLutions to linear quadratic regulator (LQR) problems for retarded systems with delay in control. For completeness, we shall also give a brief summary and discussion of an abstract approximation framework and convergence theory developed previously by Ito and Tran in[9]. In [9]we presented an approximation framework for the numerical treatment of algebraic Riccati equations for a class of linear infinite dimensional systems with unbounded input and output operators studied by Pritchard and Salamon in[19] In this paper we will call it the Pritchard-Salamon clans. This approximation theory which yields convergence of the approximating Riccati operators as well as convergence of the approximating gain operators extends earlier results developed in[7][2][8]in which the input and output operators are assumed to be bounded to the unbounded cases. The main features which distinguish the work in [9]from other work existing in the literature, see e.g.[11][14][15] are the assumptions on the smoothness of the underlined semigroup and the observation map. Because of the smoothness assumptions, the algebraic Riccati soLution has a smoothing property which in turn implies boundedness of the feedback gain operator. Although the theory developed in[9]does not cover many important boundary control problems studied by Lasiecka and Triggiani in [13] and Flandoli, Lasiecka, and Triggiani in[6] for example, it does enable us to treat the control problem governed by delay differential equations with delays in control and observation.KeywordsFeedback GainDelay Differential EquationLinear Quadratic RegulatorAlgebraic Riccati EquationBoundary Control ProblemThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
PY - 1991///
DO - 10.1007/978-1-4612-0427-5_21
SP - 307-324
OP -
PB - Birkhäuser Boston
SN - 9780817636111 9781461204275
UR - http://dx.doi.org/10.1007/978-1-4612-0427-5_21
DB - Crossref
ER -
TY - JOUR
TI - Partial Cylindrical Algebraic Decomposition for quantifier elimination
AU - Collins, George E.
AU - Hong, Hoon
T2 - Journal of Symbolic Computation
AB - The Cylindrical Algebraic Decomposition method (CAD) decomposes R r into regions over which given polynomials have constant signs. An important application of CAD is quantifier elimination in elementary algebra and geometry. In this paper we present a method which intermingles CAD construction with truth evaluation so that parts of the CAD are constructed only as needed to further truth evaluation and aborts CAD construction as soon as no more truth evaluation is needed. The truth evaluation utilizes in an essential way any quantifiers which are present and additionally takes account of atomic formulas from which some variables are absent. Preliminary observations show that the new method is always more efficient than the original, and often significantly more efficient.
DA - 1991/9//
PY - 1991/9//
DO - 10.1016/s0747-7171(08)80152-6
VL - 12
IS - 3
SP - 299-328
UR - http://dx.doi.org/10.1016/s0747-7171(08)80152-6
ER -
TY - JOUR
TI - A Fully-Discrete Spectral Method for Delay-Differential Equations
AU - Ito, K.
AU - Tran, H. T.
AU - Manitius, A.
T2 - SIAM Journal on Numerical Analysis
AB - In this paper a new Lanczos-tau method for solving linear functional differential equations is introduced. The scheme has infinite order of accuracy both in time and in the delayed argument. The high accuracy in time is obtained without increasing the computational work and memory space which is needed for a one-step explicit difference scheme. The article demonstrates how to implement the algorithm in a robust and efficient manner and to treat problems with piecewise continuous initial function. Numerical results illustrating the behavior of the method when faced with difficult problems are presented and the numerical results are compared to those obtained by using two other methods.
DA - 1991/8//
PY - 1991/8//
DO - 10.1137/0728060
VL - 28
IS - 4
SP - 1121-1140
J2 - SIAM J. Numer. Anal.
LA - en
OP -
SN - 0036-1429 1095-7170
UR - http://dx.doi.org/10.1137/0728060
DB - Crossref
KW - SPECTRAL METHOD
KW - STABILITY ANALYSIS
KW - FUNCTIONAL-DIFFERENTIAL EQUATIONS
ER -
TY - RPRT
TI - Viscous Profiles and Numerical Methods for Shock Waves
AU - Shearer, Michael
A3 - Defense Technical Information Center
DA - 1991/6/6/
PY - 1991/6/6/
DO - 10.21236/ada246110
PB - Defense Technical Information Center
UR - http://dx.doi.org/10.21236/ada246110
DB - Crossref
ER -
TY - CONF
TI - Critères de qualité en estimation ensembliste
AU - Combettes, P.L.
AU - Chaussalet, T.J.
T2 - Actes du Treizième Colloque GRETSI
C2 - 1991/9/16/
C3 - Actes du Treizième Colloque GRETSI
CY - Juan-les-Pins, France
DA - 1991/9/16/
PY - 1991/9/16/
SP - 249–252
PB - Juan-les-Pins
ER -
TY - JOUR
TI - Duality, observability, and controllability for linear time-varying descriptor systems
AU - Campbell, Stephen L.
AU - Nichols, Nancy K.
AU - Terrell, William J.
T2 - Circuits Systems and Signal Processing
DA - 1991/12//
PY - 1991/12//
DO - 10.1007/bf01194883
VL - 10
IS - 4
SP - 455-470
J2 - Circuits Systems and Signal Process
LA - en
OP -
SN - 0278-081X 1531-5878
UR - http://dx.doi.org/10.1007/bf01194883
DB - Crossref
KW - DESCRIPTOR
KW - SINGULAR
KW - DIFFERENTIAL-ALGEBRAIC
KW - OBSERVABILITY
KW - CONTROLLABILITY
KW - DUALITY
KW - STRUCTURAL FORMS
ER -
TY - JOUR
TI - Observability of Linear Time-Varying Descriptor Systems
AU - Campbell, Stephen L.
AU - Terrell, William J.
T2 - SIAM Journal on Matrix Analysis and Applications
AB - A characterization of observability for linear time-varying descriptor systems $E( t )x' ( t ) + F ( t ) x ( t ) = B (t) u (t), y ( t ) = C ( t ) x ( t )$, is given. E is not required to have constant rank. The characterization is designed to reduce symbolic computation and has potential advantages even when E is nonsingular. It is also shown that all observable analytic descriptor systems are smoothly observable even if they are not uniformly observable. Finally, the external behavior of time-varying descriptor systems is characterized.
DA - 1991/7//
PY - 1991/7//
DO - 10.1137/0612035
VL - 12
IS - 3
SP - 484-496
J2 - SIAM J. Matrix Anal. & Appl.
LA - en
OP -
SN - 0895-4798 1095-7162
UR - http://dx.doi.org/10.1137/0612035
DB - Crossref
KW - DESCRIPTOR
KW - SINGULAR
KW - OBSERVABILITY
KW - EXTERNAL BEHAVIOR
ER -
TY - JOUR
TI - Differentiation of Constraints in Differential-Algebraic Equations∗
AU - Campbell, Stephen L.
AU - Leimkuhler, B.
T2 - Mechanics of Structures and Machines
AB - ABSTRACT ABSTRACT Differentiation of constraints that appear in differential-algebraic equations (DAEs) has been advocated for many purposes, ranging from index reduction for numerical purposes to systems inversion in control theory. In this paper, the numerical and analytic consequences of such differentiations are studied and criteria are established for when difficulties can occur.
DA - 1991/1//
PY - 1991/1//
DO - 10.1080/08905459108905136
VL - 19
IS - 1
SP - 19-39
J2 - Mechanics of Structures and Machines
LA - en
OP -
SN - 0890-5452
UR - http://dx.doi.org/10.1080/08905459108905136
DB - Crossref
ER -
TY - CONF
TI - Processor efficient parallel solution of linear systems over an abstract field
AU - Kaltofen, Erich
AU - Pan, Victor
T2 - the third annual ACM symposium
AB - Article Free Access Share on Processor efficient parallel solution of linear systems over an abstract field Authors: Erich Kaltofen Department of Computer Science, Rensselaer Polytechnic Institute, Troy, New York and Department of Computer Science, University of Toronto, Toronto, Canada M5S 1A4 Department of Computer Science, Rensselaer Polytechnic Institute, Troy, New York and Department of Computer Science, University of Toronto, Toronto, Canada M5S 1A4View Profile , Victor Pan Department of Mathematics and Computer Science, Lehman College, City University of New York, Bronx, New York Department of Mathematics and Computer Science, Lehman College, City University of New York, Bronx, New YorkView Profile Authors Info & Claims SPAA '91: Proceedings of the third annual ACM symposium on Parallel algorithms and architecturesJune 1991 Pages 180–191https://doi.org/10.1145/113379.113396Online:01 June 1991Publication History 52citation350DownloadsMetricsTotal Citations52Total Downloads350Last 12 Months6Last 6 weeks2 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 SiteeReaderPDF
C2 - 1991///
C3 - Proceedings of the third annual ACM symposium on Parallel algorithms and architectures - SPAA '91
DA - 1991///
DO - 10.1145/113379.113396
PB - ACM Press
SN - 0897914384
UR - http://dx.doi.org/10.1145/113379.113396
DB - Crossref
ER -
TY - CONF
TI - Effective Noether irreducibility forms and applications
AU - Kaltofen, Erich
T2 - the twenty-third annual ACM symposium
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.
C2 - 1991///
C3 - Proceedings of the twenty-third annual ACM symposium on Theory of computing - STOC '91
DA - 1991///
DO - 10.1145/103418.103431
PB - ACM Press
SN - 0897913973
UR - http://dx.doi.org/10.1145/103418.103431
DB - Crossref
ER -
TY - JOUR
TI - On fast multiplication of polynomials over arbitrary algebras
AU - Cantor, David G.
AU - Kaltofen, Erich
T2 - Acta Informatica
DA - 1991/7//
PY - 1991/7//
DO - 10.1007/bf01178683
VL - 28
IS - 7
SP - 693-701
J2 - Acta Informatica
LA - en
OP -
SN - 0001-5903 1432-0525
UR - http://dx.doi.org/10.1007/bf01178683
DB - Crossref
ER -
TY - JOUR
TI - Vertex operators, symmetric functions, and the spin group Γn
AU - Jing, N.
T2 - Journal of Algebra
AB - This work provides a vertex operator approach to the symmetric group Sn and its double covering group Γn. By generalizing a result of Frenkel and Sato for Sn we formulate a correspondence between the space V̂ of certain twisted vertex operators, the ring Λ of symmetric functions over Q(√2), and the space of nontrivial irreducible characters of Γn. Under this identification we show that a distinguished orthogonal basis of V̂ corresponds to the set of nontrivial irreducible characters of Γn, where both are parametrized by partitions with odd integer parts. The counterpart of this distinguished basis in the ring Λ over Q(√2) is the set of Schur's Q-functions, which are, loosely speaking, the square roots of the Schur functions. The nontrivial part of the character table of Γn is shown to be given by certain matrix coefficients in V̂.
DA - 1991///
PY - 1991///
DO - 10.1016/0021-8693(91)90177-A
VL - 138
IS - 2
SP - 340-398
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-0001056353&partnerID=MN8TOARS
ER -
TY - JOUR
TI - Vertex operators and Hall-Littlewood symmetric functions
AU - Jing, N.
T2 - Advances in Mathematics
AB - We consider vertex operators on space V with a parameter t . Their components form an associative algebra which is a generalization of the Clifford algebra. A distinguished orthogonal basis of V is proved to be the Hall-Littlewood symmetric functions. We show that Kostka-Foulkes polynomials (or certain Kazhdan-Lusztig polynomials for the affine Weyl group of type A ) are matrix coefficients on the space V . We also obtain certain generating functions for the product of Hall-Littlewood functions and the Kostka-Foulkes polynomials.
DA - 1991///
PY - 1991///
DO - 10.1016/0001-8708(91)90072-F
VL - 87
IS - 2
SP - 226-248
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-0001443775&partnerID=MN8TOARS
ER -
TY - JOUR
TI - A new quantum group associated with a 'nonstandard' braid group representation
AU - Jing, N.
AU - Ge, M.-L.
AU - Wu, Y.-S.
T2 - Letters in Mathematical Physics
AB - A new quantum group is derived from a ‘nonstandard’ braid group representation by employing the Faddeev-Reshetikhin-Takhtajan constructive method. The classical limit is not a Lie superalgebra, despite relations like x 2−y 2=0. We classify all finite-dimensional irreducible representations of the new Hopf algebra and find only one- and two-dimensional ones.
DA - 1991///
PY - 1991///
DO - 10.1007/BF00420369
VL - 21
IS - 3
SP - 193-203
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-0002346824&partnerID=MN8TOARS
ER -
TY - CONF
TI - The foundations of set theoretic estimation
AU - Combettes, P.L.
AU - Civanlar, M.R.
T2 - ICASSP 91: 1991 International Conference on Acoustics, Speech, and Signal Processing
AB - Many scattered estimation problems in systems science and signal processing have been approached in set theoretic terms over the past three decades. A single formal framework is presented to synthesize these various approaches, and the fundamental philosophy, goals, and analytical techniques of set theoretic estimation are discussed.< >
C2 - 1991///
C3 - [Proceedings] ICASSP 91: 1991 International Conference on Acoustics, Speech, and Signal Processing
CY - Toronto, Ontario, Canada
DA - 1991///
PY - 1991/4/14/
DO - 10.1109/icassp.1991.151014
PB - IEEE
SN - 0780300033
UR - http://dx.doi.org/10.1109/icassp.1991.151014
ER -
TY - JOUR
TI - An algorithm for the numerical solution of equations
describing processes in photoreceivers
AU - Karamzin, Yu. N.
AU - Trofimov, V. A.
AU - Chertok, A. È.
T2 - Mat. Model.
DA - 1991///
PY - 1991///
VL - 3
IS - 10
SP - 95-103
ER -
TY - CONF
TI - Exact Transfer of Boundary Conditions in
Subsonic Problems of Computational Gas Dynamics
AU - Tsynkov, S. V.
T2 - Keldysh Institute of Applied Mathematics, USSR Academy of Sciences
A2 - Zabrodin, A. V.
A2 - Voskresensky, G. P.
C2 - 1991///
C3 - Construction of Algorithms and Solution of Mathematical Physics Problems
CY - Moscow
DA - 1991///
SP - 194-198
N1 - [in Russian]
RN - [in Russian]
ER -
TY - JOUR
TI - Decomposition algorithms based on boundary equations with
projectors
T2 - Akad. Nauk SSSR Inst. Prikl. Mat. Preprint
DA - 1991///
PY - 1991///
IS - 113
SP - 23
UR - https://mathscinet.ams.org/mathscinet-getitem?mr=1278546
N1 - [in Russian]
RN - [in Russian]
ER -
TY - JOUR
TI - Boundary equations with projectors in composite domains
T2 - Akad. Nauk SSSR Inst. Prikl. Mat. Preprint
DA - 1991///
PY - 1991///
IS - 112
SP - 20
UR - https://mathscinet.ams.org/mathscinet-getitem?mr=1278545
N1 - [in Russian]
RN - [in Russian]
ER -
TY - JOUR
TI - Application of a model of potential flow to the formulation of
conditions on the outer boundary for Euler equations. II
AU - Sofronov, I. L.
AU - Tsynkov, S. V.
T2 - Akad. Nauk SSSR Inst. Prikl. Mat. Preprint
DA - 1991///
PY - 1991///
IS - 41
SP - 27
UR - https://mathscinet.ams.org/mathscinet-getitem?mr=1156344
N1 - [in Russian]
RN - [in Russian]
ER -
TY - JOUR
TI - Application of a model of potential flow to the formulation of
conditions on the outer boundary for Euler equations. I
AU - Tsynkov, S. V.
T2 - Akad. Nauk SSSR Inst. Prikl. Mat. Preprint
DA - 1991///
PY - 1991///
IS - 40
SP - 25
UR - https://mathscinet.ams.org/mathscinet-getitem?mr=1156343
N1 - [in Russian]
RN - [in Russian]
ER -
TY - JOUR
TI - Kinetically consistent difference schemes in curvilinear
coordinate systems
AU - Elizarova, T. G.
AU - Tsynkov, S. V.
AU - Chetverushkin, B. N.
T2 - Differentsiaļprime nye Uravneniya
DA - 1991///
PY - 1991///
VL - 27
IS - 7
SP - 1161-1169, 1285
UR - https://mathscinet.ams.org/mathscinet-getitem?mr=1127501
N1 - [in Russian]
RN - [in Russian]
ER -
TY - JOUR
TI - The use of noise properties in set theoretic estimation
AU - Combettes, P.L.
AU - Trussell, H.J.
T2 - IEEE Transactions on Signal Processing
AB - In most digital signal processing problems, the goal is to estimate an object from noise corrupted observations of a physical system. The authors describe how a wide range of probabilistic information pertaining to the noise process can be used in a general set theoretic estimation framework. The basic principle is to constrain the sample statistics of the estimation residual to be consistent with those probabilistic properties of the noise which are available and to construct sets accordingly in the solution space. Adding these sets to the collection of sets describing the solution will yield a smaller feasibility set and, hence, more reliable estimates. Pieces of information relative to quantities such as range, moments, absolute moments, and second and higher order probabilistic attributes are considered, and properties of the corresponding sets are established. Simulations are provided to illustrate the theoretical developments.< >
DA - 1991/7//
PY - 1991/7//
DO - 10.1109/78.134400
VL - 39
IS - 7
SP - 1630-1641
J2 - IEEE Trans. Signal Process.
OP -
SN - 1053-587X
UR - http://dx.doi.org/10.1109/78.134400
DB - Crossref
ER -
TY - JOUR
TI - Set theoretic estimation by random search
AU - Combettes, P.L.
AU - Trussell, H.J.
T2 - IEEE Transactions on Signal Processing
AB - An adapted random search algorithm is shown to be a feasible method for the synthesis of set theoretic estimates. It circumvents the theoretical and computational shortcomings of existing deterministic methods and does not place any geometrical restrictions on the sets. The proposed method can handle arbitrarily complex property sets in applications for which the number of unknown parameters is typically low (e.g. parametric multidimensional spectral estimation, system identification, blur identification, and filter design). >
DA - 1991/7//
PY - 1991/7//
DO - 10.1109/78.134403
VL - 39
IS - 7
SP - 1669-1671
J2 - IEEE Trans. Signal Process.
OP -
SN - 1053-587X
UR - http://dx.doi.org/10.1109/78.134403
DB - Crossref
ER -
TY - CONF
TI - Yield Optimization Using a {GaAs} Process Simulator Coupled to a Physical Device Model
AU - Stoneking, D E
AU - Bilbro, G L
AU - Trew, R J
AU - Gilmore, P
AU - Kelley, C T
T2 - IEEE
C2 - 1991///
C3 - Proceedings IEEE/Cornell Conference on Advanced Concepts in High Speed Devices and Circuits
DA - 1991///
SP - 374-383
ER -
TY - CONF
TI - Simulated Performance Optimization of {GaAs} {MESFET} Amplifiers
AU - Winslow, T A
AU - Trew, R J
AU - Gilmore, P
AU - Kelley, C T
T2 - IEEE
C2 - 1991///
C3 - Proceedings IEEE/Cornell Conference on Advanced Concepts in High Speed Devices and Circuits
DA - 1991///
SP - 393-402
ER -
TY - JOUR
TI - Observations on Computational Mathematics in {J}apan
AU - Kahaner, David K
AU - Kelley, C T
T2 - ONRFE Scientific Information Bulletin
DA - 1991///
PY - 1991///
VL - 16
SP - 49-54
ER -
TY - CONF
TI - Doping Profiles For Optimum Class {B} Performance of {GaAs} MESFET Amplifiers
AU - Winslow, T A
AU - Trew, R J
AU - Gilmore, P
AU - Kelley, C T
T2 - IEEE
C2 - 1991///
C3 - Proceedings IEEE/Cornell Conference on Advanced Concepts in High Speed Devices and Circuits
DA - 1991///
SP - 188-197
ER -
TY - CONF
TI - A Study of Electron Transit-Time in Ballistic Diodes Using a Multi-Valley Hydrodynamic Transport Model
AU - Woolard, D L
AU - Trew, R J
AU - Littlejohn, M A
AU - Kelley, C T
T2 - IEEE
C2 - 1991///
C3 - Proceedings IEEE/Cornell Conference on Advanced Concepts in High Speed Devices and Circuits
DA - 1991///
SP - 131-140
ER -
TY - JOUR
TI - Comments on 2-D descriptor systems
AU - Campbell, Stephen L.
T2 - Automatica
AB - Abstract This paper discusses general 2-D descriptor systems of the form Ex i +1, j +1 = Ax i , j + Bx i +1, j + Cx i , j +1 + D 0 u i , j + D 1 u i +1, j + D 2 u i , j +1 . Solution formula and structural forms are developed for several large classes of 2-D descriptor systems. The idea of a recursive chain is introduced. It is shown that these systems include several types of behavior not discussed elsewhere in the literature.
DA - 1991/1//
PY - 1991/1//
DO - 10.1016/0005-1098(91)90020-3
VL - 27
IS - 1
SP - 189-192
J2 - Automatica
LA - en
OP -
SN - 0005-1098
UR - http://dx.doi.org/10.1016/0005-1098(91)90020-3
DB - Crossref
KW - BOUNDARY-VALUE PROBLEM
KW - DIFFERENCE EQUATIONS
KW - DISCRETE SYSTEMS
KW - MULTIDIMENSIONAL SYSTEMS
KW - LINEAR SYSTEMS
ER -
TY - JOUR
TI - A New Proof of Superlinear Convergence for Broyden’s Method in Hilbert Space
AU - Kelley, C. T.
AU - Sachs, E. W.
T2 - SIAM Journal on Optimization
AB - Broyden’s method is an extension of the secant method for an equation in one real variable to an arbitrary Hilbert space setting. It is a result of Griewank that the Broyden iterates converge locally superlinearly to a root if, in addition to the assumptions needed in finite dimension, the initial approximation for the Frechet derivative differs from the Frechet derivative at the root only by a compact operator. In this paper a new and much simpler proof of this theorem is given based on the concept of collective compactness.
DA - 1991/2//
PY - 1991/2//
DO - 10.1137/0801011
VL - 1
IS - 1
SP - 146-150
J2 - SIAM J. Optim.
LA - en
OP -
SN - 1052-6234 1095-7189
UR - http://dx.doi.org/10.1137/0801011
DB - Crossref
KW - Broyden's method
KW - superlinear convergence
KW - collective compactness
ER -
TY - JOUR
TI - Fast Algorithms for Compact Fixed Point Problems with Inexact Function Evaluations
AU - Kelley, C. T.
AU - Sachs, E. W.
T2 - SIAM Journal on Scientific and Statistical Computing
AB - A class of fast algorithms for computation of fixed points of completely continuous maps on Banach spaces is described and analyzed. These algorithms are motivated by parabolic boundary control problems where the time integration is done by a high order backward difference formula, a variable stepsize, variable order method, or a combination of such methods. In these cases, the nonlinear maps do not have the smoothness or collective compactness properties required by known fast algorithms. This paper shows how a multilevel technique of Atkinson can be modified to attack such problems, discusses how quasi-Newton methods can improve performance, and finally, shows how this approach can be applied to parabolic boundary control problems.
DA - 1991/7//
PY - 1991/7//
DO - 10.1137/0912038
VL - 12
IS - 4
SP - 725-742
J2 - SIAM J. Sci. and Stat. Comput.
LA - en
OP -
SN - 0196-5204 2168-3417
UR - http://dx.doi.org/10.1137/0912038
DB - Crossref
KW - COLLECTIVE COMPACTNESS
KW - PARABOLIC CONTROL PROBLEMS
KW - METHOD OF LINES
KW - QUASI-NEWTON METHODS
ER -
TY - JOUR
TI - Sequential quadratic programming for certain parameter identification problems
AU - Kelley, C. T.
AU - Wright, S. J.
T2 - Mathematical Programming
DA - 1991/7//
PY - 1991/7//
DO - 10.1007/bf01586941
VL - 51
IS - 1-3
SP - 281-305
J2 - Mathematical Programming
LA - en
OP -
SN - 0025-5610 1436-4646
UR - http://dx.doi.org/10.1007/bf01586941
DB - Crossref
KW - SEQUENTIAL QUADRATIC PROGRAMMING
KW - PARAMETER IDENTIFICATION
ER -
TY - JOUR
TI - Pointwise quasi-Newton method for unconstrained optimal control problems, II
AU - Kelley, C. T.
AU - Sachs, E. W.
AU - Watson, B.
T2 - Journal of Optimization Theory and Applications
DA - 1991/12//
PY - 1991/12//
DO - 10.1007/bf00941402
VL - 71
IS - 3
SP - 535-547
J2 - J Optim Theory Appl
LA - en
OP -
SN - 0022-3239 1573-2878
UR - http://dx.doi.org/10.1007/bf00941402
DB - Crossref
KW - QUASI-NEWTON METHODS
KW - OPTIMAL CONTROL
ER -
TY - JOUR
TI - Mesh Independence of Newton-like Methods for Infinite Dimensional Problems
AU - Kelley, C.T.
AU - Sachs, E.W.
T2 - Journal of Integral Equations and Applications
AB - Globally convergent modifications of Newton’s method, such as the Armijo rule, can be applied to infinite dimensional problems and their discretizations. We show that if the construction of the discretizations is done properly, then the convergence behavior of the iteration is the same for the discrete problems as it is for the infinite-dimensional problem. Basic to these results is the use of the concept of discrete convergence as a tool to measure the performance of algorithms and a new setting of Banach spaces with incomplete metrics, for example, norms generated by continuous inner products. The motivating problems are integral equations with continuous kernels. This result extends to the globally convergent case results of Allgower, Bohmer, Potra, and Rheinboldt, and the authors. In addition, we strengthen the previous results on mesh independence of quasi-Newton methods. Numerical results are reported that illustrate the results.
DA - 1991/12//
PY - 1991/12//
DO - 10.1216/jiea/1181075649
VL - 3
IS - 4
SP - 549-573
J2 - J. Integral Equations Appl.
LA - en
OP -
SN - 0897-3962
UR - http://dx.doi.org/10.1216/jiea/1181075649
DB - Crossref
ER -
TY - JOUR
TI - On a numerical algorithm for nonlinear differential equations describing some processes in photoreceivers
AU - Chertock, A.
AU - Karamzin, Y.
AU - Trofimov, V.
T2 - Journal of Mathematical Modeling
DA - 1991///
PY - 1991///
VL - 3
SP - 95–103
ER -
TY - JOUR
TI - Kinetic-Consistent Finite-Difference Schemes in Curvilinear Coordinate Systems
AU - Elizarova, T.G.
AU - Tsynkov, S.V.
AU - Chetverushkin, B.N.
T2 - Differential Equations
DA - 1991///
PY - 1991///
VL - 27
IS - 7
SP - 1161–1169
ER -
TY - JOUR
TI - Theory of wave activity occurring in the AMPTE artificial comet
AU - Bingham, R.
AU - Shapiro, V. D.
AU - Tsytovich, V. N.
AU - de Angelis, U.
AU - Gilman, M.
AU - Shevchenko, V. I.
T2 - Physics of Fluids B: Plasma Physics
AB - One of the main experiments of the Active Magnetospheric Particle Tracer Explorers (AMPTE) [J. Geophys. Res. 91, 10013 (1986)] satellite mission was the release of neutral barium atoms in the solar wind. The barium atoms ionized by photoionization extremely rapidly forming a dense, expanding, plasma cloud that interrupted the solar wind flow creating diamagnetic cavities. On the upstream side of the cavity a region of compressed plasma and enhanced magnetic field was created as the result of being produced by the slowing down and deflection of the solar wind, and magnetic field line draping. Intense electrostatic and magnetic turbulence was observed by both the IRM [J. Geophys. Res. 91, 10 013 (1986)] and UKS [J. Geophys. Res. 91, 1320 (1986)] satellites at the boundary of the diamagnetic cavity, with the most intense waves being detected near the outer boundary of the compressed region. This paper examines how the newly created expanding plasma couples to the solar wind by means of plasma–beam and current‐driven instabilities. In particular, it is shown how lower‐hybrid and lower‐hybrid drift waves are generated by cross‐field proton–barium streaming instabilities and cross‐field electron currents. The saturation mechanism for these waves is considered to be the modulational instability, this instability can also lead to filamentation and coupling to magnetosonic modes, which are also observed. As the result of modulational instability the k∥ component increases, which allows the heating and acceleration of electrons that is consistent with the observations.
DA - 1991/7//
PY - 1991/7//
DO - 10.1063/1.859984
VL - 3
IS - 7
SP - 1728-1738
J2 - Physics of Fluids B: Plasma Physics
LA - en
OP -
SN - 0899-8221
UR - http://dx.doi.org/10.1063/1.859984
DB - Crossref
ER -
TY - CHAP
TI - Some Remarks on the Generalised Bareiss and Levinson Algorithms
AU - Ipsen, Ilse
T2 - Numerical Linear Algebra, Digital Signal Processing and Parallel Algorithms
PY - 1991///
DO - 10.1007/978-3-642-75536-1_10
SP - 189-214
OP -
PB - Springer Berlin Heidelberg
SN - 9783642755385 9783642755361
UR - http://dx.doi.org/10.1007/978-3-642-75536-1_10
DB - Crossref
ER -
TY - RPRT
TI - Perturbation Theory for the Solution of Systems of Linear Equations
AU - Chandrasekaran, Shivkumar
AU - Ipsen, Ilse
A3 - Defense Technical Information Center
AB - Abstract : We present expressions for absolute and relative errors in individual components of the solution to systems of linear equations. We consider three kinds of linear systems: non-singular, underdetermined of full row rank, and least squares of full column rank. No assumptions regarding the structure or distribution of the perturbations are required. Our expressions for component- wise relative errors allow the following conclusions: For any linear system there is at least one solution component whose sensitivity to perturbations is proportional to the condition number of the matrix; but - depending on the relation between right-hand side and matrix - there may exist components that are much better conditioned. For a least squares problem, the sensitivity of the components also depends on the right-hand side and may be as high as the square of the condition number. Least squares problems are therefore always more receptive to ill-conditioning than linear systems. In addition, we show that the component-wise relative errors for linear systems are reduced by column scaling only if column scaling manages to reduce the perturbations. Regarding underdetermined linear systems of full column rank, the problem of finding the minimal-norm solution can be formulated so that the same analysis as for least squares problems is applicable here as well. Finally, we define component-wise condition numbers that measure the sensitivity of the solution components to perturbations. They have simple geometric interpretations and can be command estimated as efficiently as the conventional condition numbers.
DA - 1991/10/1/
PY - 1991/10/1/
DO - 10.21236/ada254994
PB - Defense Technical Information Center
UR - http://dx.doi.org/10.21236/ada254994
DB - Crossref
ER -
TY - JOUR
TI - The Sinc-Galerkin Method for Fourth-Order Differential Equations
AU - Smith, Ralph C.
AU - Bogar, Gary A.
AU - Bowers, Kenneth L.
AU - Lund, John
T2 - SIAM Journal on Numerical Analysis
AB - The Sinc-Galerkin method originally proposed by Stenger is extended to handle fourth-order ordinary differential equations. The exponential convergence rate of the method, $O(e^{ - \kappa \sqrt M } )$ is carefully developed and the special features of the discrete system are described. Spectral properties and conditioning of the associated matrices are given. The appropriate choice of weight function in the Galerkin inner product is discussed with primary emphasis given to choices that are best suited to fourth-order partial differential equations. Numerical results are included to help illustrate the parameter selections made and confirm the efficiency and accuracy of the method.
DA - 1991/6//
PY - 1991/6//
DO - 10.1137/0728041
VL - 28
IS - 3
SP - 760-788
J2 - SIAM J. Numer. Anal.
LA - en
OP -
SN - 0036-1429 1095-7170
UR - http://dx.doi.org/10.1137/0728041
DB - Crossref
KW - SINC-GALERKIN
KW - 4TH-ORDER DIFFERENTIAL EQUATIONS
ER -