TY - JOUR
TI - Curves on $S^{n - 1} $ That Lead to Eigenvalues or Their Means of a Matrix
AU - Chu, Moody T.
T2 - SIAM Journal on Algebraic Discrete Methods
AB - This paper discusses two dynamical systems on the unit sphere $S^{n - 1} $ in $\mathbb{R}^n $ space, each defined in terms of a real square matrix M. The solutions of these systems are found to converge to points which provide essential information about eigenvalues of the matrix M. It is shown, in particular, how the dynamics of the second flow is analogous to that of the Rayleigh quotient iterations.
DA - 1986/7//
PY - 1986/7//
DO - 10.1137/0607048
VL - 7
IS - 3
SP - 425-432
UR - http://dx.doi.org/10.1137/0607048
ER -
TY - JOUR
TI - A differential equation approach to the singular value decomposition of bidiagonal matrices
AU - Chu, M.T.
T2 - Linear Algebra and Its Applications
AB - We consider the problem of approximating the singular value decomposition of a bidiagonal matrix by a one-parameter family of differentiable matrix flows. It is shown that this approach can be fully expressed as an autonomous, homogeneous, and cubic dynamical system. Asymptotic behavior is justified by the established theory of the Toda lattice.
DA - 1986///
PY - 1986///
DO - 10.1016/0024-3795(86)90278-8
VL - 80
IS - C
SP - 71-79
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-0002063624&partnerID=MN8TOARS
ER -
TY - JOUR
TI - A continuous approximation to the generalized Schur decomposition
AU - Chu, M.
T2 - Linear Algebra and Its Applications
AB - We consider the problem of approximating the generalized Schur decomposition of a matrix pencil A − λB by a family of differentiable orthogonal transformations. It is shown that when B is nonsingular this approach is feasible and can be fully expressed as an autonomous differential system. When B is singular, we show that the location of zero diagonal entries of B affects the feasibility of such an approach, and hence we conclude that at least the QZ algorithm cannot be extended continuously.
DA - 1986///
PY - 1986///
DO - 10.1016/0024-3795(86)90019-4
VL - 78
IS - C
SP - 119-132
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-0038953719&partnerID=MN8TOARS
ER -
TY - CHAP
TI - Consistent initial conditions for linear time varying singular systems
AU - Campbell, Stephen L.
T2 - Frequency Domain and State Space Methods for Linear Systems
A2 - Byrnes, C. I.
A2 - Lindquist, A.
PY - 1986///
SP - 313–318
PB - Elsevier
SN - 9780444700384
ER -
TY - CHAP
TI - Three phase flow in porous media-recent developments in nonstrictly hyperbolic conservation laws
AU - Shearer, Michael
AU - Schaeffer, D.G.
T2 - Advances in Multiphase Flow and Related Problems
A2 - Papanicolaou, G.
PY - 1986///
SP - 210-218
PB - SIAM
ER -
TY - CONF
TI - Recent developments in nonstrictly hyperbolic conservation laws
AU - Shearer, Michael
AU - Schaeffer, D.G.
T2 - 4th Army Conference on Applied Mathematics and Computing
C2 - 1986/5//
C3 - Transactions of the Fourth Army Conference on Applied Mathematics and Computing
CY - Cornell University, Ithaca, New York
DA - 1986/5//
PY - 1986/5/27/
PB - U.S. Army Research Office
ER -
TY - CONF
TI - Shock waves and bifurcation
AU - Shearer, Michael
A2 - Gama, L.
C2 - 1986///
C3 - Proceedings of the Brazilian National Colloquium
DA - 1986///
ER -
TY - RPRT
TI - Systolic implementation of a Toeplitz system solver
AU - Delosme, J.-M.
AU - Ipsen, I.C.F.
AU - Masse, J.-R.
A3 - Department of Electrical Engineering, Yale University
DA - 1986///
PY - 1986///
M1 - 8607
M3 - Research Report
PB - Department of Electrical Engineering, Yale University
SN - 8607
ER -
TY - CHAP
TI - Systolic array synthesis: Computability and time cones
AU - Delosme, J.-M.
AU - Ipsen, I.C.F.
T2 - Parallel Algorithms and Architectures
PY - 1986///
SP - 295–312
PB - North-Holland Publishing
ER -
TY - JOUR
TI - Numerical simulation of a non-linear feedback controller for a wind tunnel model involving a time delay
AU - Manitius, A.
AU - Tran, H.
T2 - Optimal Control Applications and Methods
AB - This paper describes a non-linear, S-minimum time, feedback controller for a wind tunnel model and a numerical simulation of its performance. The model is a linear third-order system with delay and a state-variable constraint; it represents the dynamics of a Mach number control loop in a cryogenic wind tunnel. The design method involves a singular perturbation technique, an impulse control and a compensation of delay. Peformance of linear and non-linear S-minimum time control is compared in various operating conditions. The closed-loop dynamics of the non-linear system is examined by numerical simulations which exhibit the boundary-layer phenomena in the control and the effects of various changes in parameters.
DA - 1986/1//
PY - 1986/1//
DO - 10.1002/oca.4660070103
VL - 7
IS - 1
SP - 19-39
J2 - Optim. Control Appl. Meth.
LA - en
OP -
SN - 0143-2087 1099-1514
UR - http://dx.doi.org/10.1002/oca.4660070103
DB - Crossref
ER -
TY - JOUR
TI - Eigenvalues and eigenvectors of large-dimensional sample covariance matrices
AU - Silverstein, Jack W.
T2 - Random Matrices and Their Applications
DA - 1986///
PY - 1986///
DO - 10.1090/conm/050/841089
VL - 50
SP - 153-159
SN - 1098-3627 0271-4132
UR - http://dx.doi.org/10.1090/conm/050/841089
ER -
TY - JOUR
TI - Nonuniqueness of admissible solutions of Riemann initial value problems for a system of conservation laws of mixed type
AU - Shearer, Michael
T2 - Archive for Rational Mechanics and Analysis
DA - 1986/3//
PY - 1986/3//
DO - 10.1007/bf00250844
VL - 93
IS - 1
SP - 45-59
J2 - Arch. Rational Mech. Anal.
LA - en
OP -
SN - 0003-9527 1432-0673
UR - http://dx.doi.org/10.1007/bf00250844
DB - Crossref
ER -
TY - JOUR
TI - The Riemann problem for the planar motion of an elastic string
AU - Shearer, Michael
T2 - Journal of Differential Equations
AB - where T= 7’( Ir,l) is the tension in the string, taken here to be a given smooth monotonically increasing function of the stretch 1~~~1 alone. In (l.l), we have also taken the density of the material of the string to be constant. The derivation of Eq. (1.1) (and of more general equations of motion for the string) is explained in [l]. In a previous paper [5], the Riemann problem was solved for system ( 1.1) under two assumptions: that the graph of T has exactly one inflection point, at t,, with
DA - 1986/2//
PY - 1986/2//
DO - 10.1016/0022-0396(86)90116-6
VL - 61
IS - 2
SP - 149-163
J2 - Journal of Differential Equations
LA - en
OP -
SN - 0022-0396
UR - http://dx.doi.org/10.1016/0022-0396(86)90116-6
DB - Crossref
ER -
TY - JOUR
TI - Index two linear time varying singular systems of differential equations
AU - Campbell, Stephen L.
T2 - Circuits, Systems, and Signal Processing
DA - 1986/3//
PY - 1986/3//
DO - 10.1007/bf01600189
VL - 5
IS - 1
SP - 97-107
J2 - Circuits Systems and Signal Process
LA - en
OP -
SN - 0278-081X 1531-5878
UR - http://dx.doi.org/10.1007/bf01600189
DB - Crossref
ER -
TY - JOUR
TI - Countability of Sets
AU - Campbell, Stephen L.
T2 - The American Mathematical Monthly
DA - 1986/6//
PY - 1986/6//
DO - 10.1080/00029890.1986.11971864
VL - 93
IS - 6
SP - 480-481
J2 - The American Mathematical Monthly
LA - en
OP -
SN - 0002-9890 1930-0972
UR - http://dx.doi.org/10.1080/00029890.1986.11971864
DB - Crossref
ER -
TY - CHAP
TI - Efficient parallel evaluation of straight-line code and arithmetic circuits
AU - Miller, Gary L
AU - Ramachandran, Vijaya
AU - Kaltofen, Erich
T2 - VLSI Algorithms and Architectures
PY - 1986///
DO - 10.1007/3-540-16766-8_21
SP - 236-245
OP -
PB - Springer Berlin Heidelberg
SN - 9783540167662 9783540387466
UR - http://dx.doi.org/10.1007/3-540-16766-8_21
DB - Crossref
ER -
TY - CONF
TI - Uniform closure properties of P-computable functions
AU - Kaltofen, E
T2 - the eighteenth annual ACM symposium
AB - Article Uniform closure properties of P-computable functions Share on Author: E Kaltofen Rensselaer Polytechnic Institute, Dept. of Computer Science, Troy, New York and Mathematical Sciences Research Institute, Berkeley, California Rensselaer Polytechnic Institute, Dept. of Computer Science, Troy, New York and Mathematical Sciences Research Institute, Berkeley, CaliforniaView Profile Authors Info & Claims STOC '86: Proceedings of the eighteenth annual ACM symposium on Theory of computingNovember 1986 Pages 330–337https://doi.org/10.1145/12130.12163Online:01 November 1986Publication History 12citation239DownloadsMetricsTotal Citations12Total Downloads239Last 12 Months4Last 6 weeks0 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 - 1986///
C3 - Proceedings of the eighteenth annual ACM symposium on Theory of computing - STOC '86
DA - 1986///
DO - 10.1145/12130.12163
PB - ACM Press
SN - 0897911938
UR - http://dx.doi.org/10.1145/12130.12163
DB - Crossref
ER -
TY - CONF
TI - A system for manipulating polynomials given by straight-line programs
AU - Freeman, T.
AU - Imirzian, G.
AU - Kaltofen, E.
T2 - the fifth ACM symposium
AB - We discuss the design, implementation, and benchmarking of a system that can manipulate symbolic expressions represented by their straight-line computations. Our system is capable of performing rational arithmetic, evaluating, differentiating, taking greatest common divisors of, and factoring polynomials in straight-line format. The straight-line results can also be converted to standard sparse format. We show by example that our system can handle problems for which conventional methods lead to excessive intermediate expression swell.
C2 - 1986///
C3 - Proceedings of the fifth ACM symposium on Symbolic and algebraic computation - SYMSAC '86
DA - 1986///
DO - 10.1145/32439.32473
PB - ACM Press
SN - 0897911997
UR - http://dx.doi.org/10.1145/32439.32473
DB - Crossref
ER -
TY - CONF
TI - Fast parallel algorithms for similarity of matrices
AU - Kaltofen, E.
AU - Krishnamoorthy, M.
AU - Saunders, B. D.
T2 - the fifth ACM symposium
AB - Article Fast parallel algorithms for similarity of matrices Share on Authors: E. Kaltofen Rensselaer Polytechnic Institute, Troy, NY Rensselaer Polytechnic Institute, Troy, NYView Profile , M. Krishnamoorthy Univ. of Delaware, Newark Univ. of Delaware, NewarkView Profile , B. D. Saunders Math. Sci. Research Inst., Berkeley, CA Math. Sci. Research Inst., Berkeley, CAView Profile Authors Info & Claims SYMSAC '86: Proceedings of the fifth ACM symposium on Symbolic and algebraic computationOctober 1986 Pages 65–70https://doi.org/10.1145/32439.32452Published:01 October 1986 6citation196DownloadsMetricsTotal Citations6Total Downloads196Last 12 Months0Last 6 weeks0 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 - 1986///
C3 - Proceedings of the fifth ACM symposium on Symbolic and algebraic computation - SYMSAC '86
DA - 1986///
DO - 10.1145/32439.32452
PB - ACM Press
SN - 0897911997
UR - http://dx.doi.org/10.1145/32439.32452
DB - Crossref
ER -
TY - JOUR
TI - Convergence of the {F_N} method for multi-group transport
AU - Kelley, C T
T2 - Trans. Th. Stat. Phys.
DA - 1986///
PY - 1986///
VL - 15
SP - 821-828
ER -
TY - JOUR
TI - A Shamanskii-like acceleration scheme for nonlinear equations at singular roots
AU - Kelley, C.T.
T2 - Mathematics of Computation
DA - 1986///
PY - 1986///
VL - 47
IS - 176
SP - 609–623
ER -
TY - RPRT
TI - Progress Report Number 2 on Contract AFOSR-84-0240.
AU - Campbell, Stephen L.
A3 - Defense Technical Information Center
AB - Abstract : Implicit systems of differential equations of the form F(t,y,y') = 0 naturally arise in many circuit and control problems, economic models, and the solution of partial differential equations by the method of lines. Implicit systems are also called singular, differential-algebraic, semi-state, constrained, and descriptor. The theory is well understood, and numerical codes exist, for index zero, index one, and linear constant coefficient problems. Higher index systems occur in circuit and control problems. The numerical and analytic behavior of such higher index systems is not well understood and is incomplete. It has recently been shown that traditional methods, such as backward differences, need not work on higher index systems. Good characterizations of the solution manifold are often difficult to obtain. This research project is to study the numerical and analytic solution of higher index implicit differential equations. Applications will be made to circuit theory, control theory, and the analysis of numerically ill-conditioned index one systems.
DA - 1986/1/1/
PY - 1986/1/1/
DO - 10.21236/ada172881
PB - Defense Technical Information Center
ER -
TY - JOUR
TI - Vector algorithms for H-equations arising in radiative transfer through inhomogeneous media
AU - Hollis, S. L.
AU - Kelley, C. T.
T2 - Transport Theory and Statistical Physics
AB - Abstract The exit distribution problem for one speed isotropic radiative transfer in an inhomogeneous slab can be solved in terms of an analog of the Chandrasekhar H-Function. This function is the solution to a nonlinear integral equation in two variables for one group problems and in more variables for multi-group problems. In this paper we give algorithms for vector computers, in particular the CDC Cyber 205, that make it practical to solve such equations.
DA - 1986/2//
PY - 1986/2//
DO - 10.1080/00411458608210443
VL - 15
IS - 1-2
SP - 33-48
J2 - Transport Theory and Statistical Physics
LA - en
OP -
SN - 0041-1450 1532-2424
UR - http://dx.doi.org/10.1080/00411458608210443
DB - Crossref
ER -
TY - JOUR
TI - Convergence of the FN - method for multi-group transport
AU - Kelley, C. T.
T2 - Transport Theory and Statistical Physics
AB - Abstract This note extends previous results of Mullikin and the author on convergence of the FN method to isotropic multi-group problems in half-space geometries.
DA - 1986/10//
PY - 1986/10//
DO - 10.1080/00411458608212717
VL - 15
IS - 6-7
SP - 821-828
J2 - Transport Theory and Statistical Physics
LA - en
OP -
SN - 0041-1450 1532-2424
UR - http://dx.doi.org/10.1080/00411458608212717
DB - Crossref
ER -
TY - JOUR
TI - Complexity of dense-linear-system solution on a multiprocessor ring
AU - Ipsen, Ilse C.F.
AU - Saad, Youcef
AU - Schultz, Martin H.
T2 - Linear Algebra and its Applications
AB - Different algorithms, based on Gaussian elimination, for the solution of dense linear systems of equations are discussed for a multiprocessor ring. The number of processors is assumed not to exceed the problem size. A fairly general model for data transfer is proposed, and the algorithms are analyzed with respect to their requirements of arithmetic as well as communication times.
DA - 1986/5//
PY - 1986/5//
DO - 10.1016/0024-3795(86)90169-2
VL - 77
IS - C
SP - 205-239
J2 - Linear Algebra and its Applications
LA - en
OP -
SN - 0024-3795
UR - http://dx.doi.org/10.1016/0024-3795(86)90169-2
DB - Crossref
ER -
TY - CHAP
TI - The Impact of Parallel Architectures on The Solution of Eigenvalue Problems
AU - Ipsen, Ilse C.F.
AU - Saad, Youcef
T2 - Large Scale Eigenvalue Problems, Proceedings of the IBM Europe Institute Workshop on Large Scale Eigenvalue Problems
AB - This paper presents a short survey of recent work on parallel implementations of Numerical Linear Algebra algorithms with emphasis on those relating to the solution of the symmetric eigenvalue problem on loosely coupled multiprocessor architectures. The vital operations in the formulation of most eigenvalue algorithms are matrix vector multiplication, matrix transposition, and linear system solution. Their implementations on several representative multiprocessor systems will be described, as well as parallel implementations of the following classes of eigenvalue methods : QR, bisection, divide-and-conquer, and Lanczos algorithm.
PY - 1986///
DO - 10.1016/s0304-0208(08)72638-0
VL - 127
SP - 37-49
OP -
PB - Elsevier
SN - 9780444700742
UR - http://dx.doi.org/10.1016/s0304-0208(08)72638-0
DB - Crossref
ER -
TY - CONF
TI - Design Methodology For Systolic Arrays
AU - Delosme, Jean-Marc
AU - Ipsen, Ilse C. F.
T2 - 30th Annual Technical Symposium
A2 - Speiser, Jeffrey M.
AB - Many important algorithms in signal and image processing, speech and pattern recognition or matrix computations consist of coupled systems of recurrence equations. Systolic arrays are regular networks of tightly coupled simple processors with limited storage that provide cost-effective high-throughput implementations of many such algorithms. While there are some mathematical techniques for finding efficient systolic implementations for uniform recurrence equations, there is no general theory for more general coupled systems of affine recurrence equations. The first elements of such a theory are presented in this paper.
C2 - 1986/4/4/
C3 - Advanced Algorithms and Architectures for Signal Processing I
DA - 1986/4/4/
DO - 10.1117/12.936899
VL - 696
SP - 245-259
PB - SPIE
UR - http://dx.doi.org/10.1117/12.936899
DB - Crossref
ER -
TY - JOUR
TI - Parallel solution of symmetric positive definite systems with hyperbolic rotations
AU - Delosme, Jean-Marc
AU - Ipsen, Ilse C.F.
T2 - Linear Algebra and its Applications
AB - An algorithm based on hyperbolic rotations is presented for the solution of linear systems of equations Ax = b, with symmetric positive definite coefficient matrix A. Forward elimination and backsubstitution are replaced by matrix-vector multiplications, rendering the method amenable to implementation on a variety of parallel and vector machines. This method can be simplified and formulated without square roots if A is also Toeplitz; a systolic (VLSI) architecture implementing the resulting recurrence equations is more efficient than previously proposed pipelined Toeplitz system solvers. The hardware count becomes independent of the matrix size if its inverse is banded.
DA - 1986/5//
PY - 1986/5//
DO - 10.1016/0024-3795(86)90163-1
VL - 77
IS - C
SP - 75-111
J2 - Linear Algebra and its Applications
LA - en
OP -
SN - 0024-3795
UR - http://dx.doi.org/10.1016/0024-3795(86)90163-1
DB - Crossref
ER -