**Contemporary Mathematics**

Volume: 281;
2001;
344 pp;
Softcover

MSC: Primary 15; 47; 65; 93;

Print ISBN: 978-0-8218-2092-6

Product Code: CONM/281

List Price: $96.00

Individual Member Price: $76.80

**Electronic ISBN: 978-0-8218-7871-2
Product Code: CONM/281.E**

List Price: $96.00

Individual Member Price: $76.80

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# Structured Matrices in Mathematics, Computer Science, and Engineering II

Share this page *Edited by *
*Vadim Olshevsky*

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 contains 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

# Table of Contents

## Structured Matrices in Mathematics, Computer Science, and Engineering II

- Contents vii8 free
- Foreword xi12 free
- Part V. Fast Algorithms 116 free
- Part VI. Numerical Issues 5570
- Stability properties of several variants of the unitary Hessenberg QR algorithm 5772
- Comparison of algorithms for Toeplitz least squares and symmetric positive definite linear systems 7388
- Stability of Toeplitz matrix inversion formulas 101116
- Necessary and sufficient conditions for accurate and efficient rational function evaluation and factorizations of rational matrices 117132
- Updating and downdating of orthonormal polynomial vectors and some applications 145160
- Rank-revealing decompositions of symmetric Toeplitz matrices 163178

- Part VII. Iterative Methods. Preconditioners 173188
- Part VIII. Linear Algebra and Various Applications 213228
- Approximate displacement rank and applications 215230
- Properties of some generalizations of Kac-Murdock-Szegö matrices 233248
- Efficient inversion formulas for Toeplitz-plus-Hankel matrices using trigonometric transformations 247262
- On a generalization of Poincaré's theorem for matrix difference equations arising from root-finding problems 265280
- Completions of triangular matrices: A survey of results and open problems 279294
- Positive representation formulas for finite difference discretizations of (elliptic) second order PDEs 295310
- On some problems involving invariant norms and Hadamard products 319334
- A generalization of the Perron-Frobenius theorem for non-linear perturbations of Stiltjes matrices 325340
- The rhombus matrix: Definition and properties 331346

#### Readership

Graduate students and research mathematicians interested in linear and multilinear algebra, matrix theory, operator theory, numerical analysis, and systems theory and control.