9780821819210

Structured Matrices in Mathematics, Computer Science, and Engineering I: Proceedings of an Ams-Ims-Siam Joint Summer Research Conference, University of Colorado, Boulder, June 27-July 1, 1999

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  • ISBN13:

    9780821819210

  • ISBN10:

    0821819216

  • Format: Paperback
  • Copyright: 2001-08-01
  • Publisher: Amer Mathematical Society

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Summary

Many important problems in applied sciences, mathematics, and engineering can be reduced to matrix problems. Moreover, various applications often introduce a special structure into the corresponding matrices, so that their entries can be described by a certain compact formula. Classic examples include Toeplitz matrices, Hankel matrices, Vandermonde matrices, Cauchy matrices, Pick matrices, Bezoutians, controllability and observability matrices, and others. Exploiting these and the more general structures often allows us to obtain elegant solutions to mathematical problems as well as to design more efficient practical algorithms for a variety of applied engineering problems. Structured matrices have been under close study for a long time and in quite diverse (and seemingly unrelated) areas, for example, mathematics, computer science, and engineering. Considerable progress has recently been made in all these areas, and especially in studying the relevant numerical and computational issues. In the past few years, a number of practical algorithms blending speed and accuracy have been developed. This significant growth is fully reflected in these volumes, which collect 38 papers devoted to the numerous aspects of the topic. The collection of the contributions to these volumes offers a flavor of the plethora of different approaches to attack structured matrix problems. The reader will find that the theory of structured matrices is positioned to bridge diverse applications in the sciences and engineering, deep mathematical theories, as well as computational and numerical issues. The presentation fully illustrates the fact that the techniques of engineers, mathematicians, and numerical analysts nicely complement each other, and they all contribute to one unified theory of structured matrices. The book is published in two volumes. The first contain s articles on interpolation, system theory, signal and image processing, control theory, and spectral theory. Articles in the second volume are devoted to fast algorithms, numerical and iterative methods, and various applications.

Table of Contents

Structured Matrices in Mathematics, Computer Science, and Engineering II
Foreword xi
Part I. Interpolation and Approximation
Structured matrices, reproducing kernels and interpolation
3(28)
H. Dym
A superfast algorithm for confluent rational tangential interpolation problem via matrix-vector multiplication for confluent Cauchy-like matrices
31(16)
V. Olshevsky
A. Shokrollahi
The maximal-volume concept in approximation by low-rank matrices
47(6)
S.A. Goreinov
E. E. Tyrtyshnikov
A matrix interpretation of the extended Euclidean algorithm
53(18)
M.H. Gutknecht
The essential polynomial approach to convergence of matrix Pade approximants
71(20)
V.M. Adukov
Part II. System Theory, Signal and Image Processing
Systems of low Hankel rank: A survey
91(12)
P. Dewilde
Tensor approximation and signal processing applications
103(32)
E. Kofidis
P. A. Regalia
Exploiting Toeplitz-like structure in adaptive filtering algorithms using signal flow graphs
135(22)
I.K. Proudler
The structured total least squares problem
157(20)
N. Mastronardi
P. Lemmerling
S. Van Huffel
Exploiting Toeplitz structure in atmospheric image restoration
177(16)
W. K. Cochran
R. J. Plemmons
T. C. Torgersen
Part III. Control Theory
A survey of model reduction methods for large-scale systems
193(28)
A. C. Antoulas
D. C. Sorensen
S. Gugercin
Theory and computations of some inverse eigenvalue problems for the quadratic pencil
221(20)
B. N. Datta
D. Sarkissian
Partial eigenvalue assignment for large linear control systems
241(14)
D. Calvetti
B. Lewis
L. Reichel
A hybrid method for the numerical solution of discrete-time algebraic Riccati equations
255(18)
H. Fassbender
P. Benner
Part IV. Spectral Properties. Conditioning
Condition numbers of large Toeplitz-like matrices
273(28)
A. Bottcher
S. Grudsky
How bad are symmetric Pick matrices?
301(12)
D. Fasino
V. Olshevsky
Spectral properties of real Hankel matrices
313(8)
M. Fiedler
Conjectures and remarks on the limit of the spectral radius of nonnegative and block Toeplitz matrices
321
L. Elsner
S. Friedland
Structured Matrices in Mathematics, Computer Science, and Engineering II
Foreword xi
Part V. Fast Algorithms
The Schur algorithm for matrices with Hessenberg displacement structure
3(14)
G. Heinig
V. Olshevsky
Fast inversion algorithms for a class of block structured matrices
17(22)
Y. Eidelman
I. Gohberg
A fast and stable solver for recursively semi-separable systems of linear equations
39(18)
S. Chandrasekaran
Ming Gu
Part VI. Numerical Issues
Stability properties of several variants of the unitary Hessenberg QR algorithm
57(16)
M. Stewart
Comparison of algorithms for Toeplitz least squares and symmetric positive definite linear systems
73(28)
M. Kim
H. Park
L. Elden
Stability of Toeplitz matrix inversion formulas
101(16)
Georg Heinig
Necessary and sufficient conditions for accurate and efficient rational function evaluation and factorizations of rational matrices
117(28)
J. Demmel
P. Koev
Updating and downdating of orthonormal polynomial vectors and some applications
145(18)
M. Van Barel
A. Bultheel
Rank-revealing decompositions of symmetric Toeplitz matrices
163(12)
P. C. Hansen
P. Yalamov
Part VII. Iterative Methods. Preconditioners
A survey of preconditioners for ill-conditioned Toeplitz systems
175(18)
R. H. Chan
M. K. Ng
A. M. Yip
Preconditioning of Hermitian block--Toeplitz--Toeplitz--block matrices by level-1 preconditioners
193(22)
D. Potts
G. Steidl
Part VIII. Linear Algebra and Various Applications
Approximate displacement rank and applications
215(18)
D. A. Bini
B. Meini
Properties of some generalizations of Kac-Murdock-Szego matrices
233(14)
W. F. Trench
Efficient inversion formulas for Toeplitz-plus-Hankel matrices using trigonometric transformations
247(18)
G. Heinig
K. Rost
On a generalization of Poincare's theorem for matrix difference equations arising from root-finding problems
265(14)
L. Gemignani
Completions of triangular matrices: A survey of results and open problems
279(16)
L. Rodman
Positive representation formulas for finite difference discretizations of (elliptic) second order PDEs
295(24)
S. Serra Capizzano
C. T. Possio
On some problems involving invariant norms and Hadamard products
319(6)
P. Tilli
A generalization of the Perron-Frobenius theorem for non-linear perturbations of Stiltjes matrices
325(6)
Y. S. Choi
I. Koltracht
P. J. McKenna
The rhombus matrix: Definition and properties
331
M. J. C. Gover
A. M. Byrne

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