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Product Code:  CONM/280.E 
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Book DetailsContemporary MathematicsVolume: 280; 2001; 327 ppMSC: Primary 15; 47; 65; 93;
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.ReadershipGraduate students and research mathematicians interested in linear and multilinear algebra, matrix theory, operator theory, numerical analysis, and systems theory and control.
This item is also available as part of a set: 
Table of Contents

Part I. Interpolation and Approximation [ MR 1850397 ]

Harry Dym  Structured matrices, reproducing kernels and interpolation [ MR 1850398 ]

Vadim Olshevsky and Amin Shokrollahi  A superfast algorithm for confluent rational tangential interpolation problem via matrixvector multiplication for confluent Cauchylike matrices [ MR 1850399 ]

S. A. Goreinov and E. E. Tyrtyshnikov  The maximalvolume concept in approximation by lowrank matrices

Martin H. Gutknecht  A matrix interpretation of the extended Euclidean algorithm [ MR 1850401 ]

Victor M. Adukov  The essential polynomial approach to convergence of matrix Padé approximants [ MR 1850402 ]

Part II. System Theory, Signal and Image Processing [ MR 1850397 ]

P. Dewilde  Systems of low Hankel rank: a survey [ MR 1850403 ]

Eleftherios Kofidis and Phillip A. Regalia  Tensor approximation and signal processing applications [ MR 1850404 ]

I. K. Proudler  Exploiting Toeplitzlike structure in adaptive filtering algorithms using signal flow graphs [ MR 1850405 ]

Nicola Mastronardi, Philippe Lemmerling and Sabine Van Huffel  The structured total least squares problem [ MR 1850406 ]

W. K. Cochran, R. J. Plemmons and T. C. Torgersen  Exploiting Toeplitz structure in atmospheric image restoration [ MR 1850407 ]

Part III. Control Theory [ MR 1850397 ]

A. C. Antoulas, D. C. Sorensen and S. Gugercin  A survey of model reduction methods for largescale systems [ MR 1850408 ]

Biswa N. Datta and Daniil R. Sarkissian  Theory and computations of some inverse eigenvalue problems for the quadratic pencil [ MR 1850409 ]

D. Calvetti, B. Lewis and L. Reichel  Partial eigenvalue assignment for large linear control systems [ MR 1850410 ]

Heike Faßbender and Peter Benner  A hybrid method for the numerical solution of discretetime algebraic Riccati equations [ MR 1850411 ]

Part IV. Spectral Properties. Conditioning [ MR 1850397 ]

A. Böttcher and S. Grudsky  Condition numbers of large Toeplitzlike matrices [ MR 1850412 ]

Dario Fasino and Vadim Olshevsky  How bad are symmetric Pick matrices? [ MR 1850413 ]

Miroslav Fiedler  Spectral properties of real Hankel matrices [ MR 1850414 ]

Ludwig Elsner and S. Friedland  Conjectures and remarks on the limit of the spectral radius of nonnegative and block Toeplitz matrices [ MR 1850415 ]


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

Part I. Interpolation and Approximation [ MR 1850397 ]

Harry Dym  Structured matrices, reproducing kernels and interpolation [ MR 1850398 ]

Vadim Olshevsky and Amin Shokrollahi  A superfast algorithm for confluent rational tangential interpolation problem via matrixvector multiplication for confluent Cauchylike matrices [ MR 1850399 ]

S. A. Goreinov and E. E. Tyrtyshnikov  The maximalvolume concept in approximation by lowrank matrices

Martin H. Gutknecht  A matrix interpretation of the extended Euclidean algorithm [ MR 1850401 ]

Victor M. Adukov  The essential polynomial approach to convergence of matrix Padé approximants [ MR 1850402 ]

Part II. System Theory, Signal and Image Processing [ MR 1850397 ]

P. Dewilde  Systems of low Hankel rank: a survey [ MR 1850403 ]

Eleftherios Kofidis and Phillip A. Regalia  Tensor approximation and signal processing applications [ MR 1850404 ]

I. K. Proudler  Exploiting Toeplitzlike structure in adaptive filtering algorithms using signal flow graphs [ MR 1850405 ]

Nicola Mastronardi, Philippe Lemmerling and Sabine Van Huffel  The structured total least squares problem [ MR 1850406 ]

W. K. Cochran, R. J. Plemmons and T. C. Torgersen  Exploiting Toeplitz structure in atmospheric image restoration [ MR 1850407 ]

Part III. Control Theory [ MR 1850397 ]

A. C. Antoulas, D. C. Sorensen and S. Gugercin  A survey of model reduction methods for largescale systems [ MR 1850408 ]

Biswa N. Datta and Daniil R. Sarkissian  Theory and computations of some inverse eigenvalue problems for the quadratic pencil [ MR 1850409 ]

D. Calvetti, B. Lewis and L. Reichel  Partial eigenvalue assignment for large linear control systems [ MR 1850410 ]

Heike Faßbender and Peter Benner  A hybrid method for the numerical solution of discretetime algebraic Riccati equations [ MR 1850411 ]

Part IV. Spectral Properties. Conditioning [ MR 1850397 ]

A. Böttcher and S. Grudsky  Condition numbers of large Toeplitzlike matrices [ MR 1850412 ]

Dario Fasino and Vadim Olshevsky  How bad are symmetric Pick matrices? [ MR 1850413 ]

Miroslav Fiedler  Spectral properties of real Hankel matrices [ MR 1850414 ]

Ludwig Elsner and S. Friedland  Conjectures and remarks on the limit of the spectral radius of nonnegative and block Toeplitz matrices [ MR 1850415 ]