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Fast Algorithms for Structured Matrices: Theory and Applications
 
Edited by: Vadim Olshevsky :  University of Connecticut, Storrs, CT
A co-publication of the AMS and Society for Industrial and Applied Mathematics
Fast Algorithms for Structured Matrices: Theory and Applications
eBook ISBN:  978-0-8218-7913-9
Product Code:  CONM/323.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $87.50
Add to cart
Fast Algorithms for Structured Matrices: Theory and Applications
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Fast Algorithms for Structured Matrices: Theory and Applications
Edited by: Vadim Olshevsky :  University of Connecticut, Storrs, CT
A co-publication of the AMS and Society for Industrial and Applied Mathematics
eBook ISBN:  978-0-8218-7913-9
Product Code:  CONM/323.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $87.50
Add to cart
  • Book Details
     
     
    Contemporary Mathematics
    Volume: 323; 2003; 433 pp
    MSC: Primary 68; 65; 15; 47

    One of the best known fast computational algorithms is the fast Fourier transform method. Its efficiency is based mainly on the special structure of the discrete Fourier transform matrix. Recently, many other algorithms of this type were discovered, and the theory of structured matrices emerged.

    This volume contains 22 survey and research papers devoted to a variety of theoretical and practical aspects of the design of fast algorithms for structured matrices and related issues. Included are several papers containing various affirmative and negative results in this direction. The theory of rational interpolation is one of the excellent sources providing intuition and methods to design fast algorithms. The volume contains several computational and theoretical papers on the topic. There are several papers on new applications of structured matrices, e.g., to the design of fast decoding algorithms, computing state-space realizations, relations to Lie algebras, unconstrained optimization, solving matrix equations, etc.

    The book is suitable for mathematicians, engineers, and numerical analysts who design, study, and use fast computational algorithms based on the theory of structured matrices.

    This volume is a joint publication of the American Mathematical Society and the Society for Industrial and Applied Mathematics.
    Readership

    Graduate students and research mathematicians interested in the theory and applications of fast numerical algorithms.
  • Table of Contents
     
     
    • Articles
    • Vadim Olshevsky — Pivoting for structured matrices and rational tangential interpolation [ MR 1999387 ]
    • Georg Heinig — Inversion of Toeplitz-plus-Hankel matrices with arbitrary rank profile [ MR 1999388 ]
    • Dario Fasino and Luca Gemignani — A Lanczos-type algorithm for the QR factorization of Cauchy-like matrices [ MR 1999389 ]
    • Dario Fasino, Nicola Mastronardi and Marc Van Barel — Fast and stable algorithms for reducing diagonal plus semiseparable matrices to tridiagonal and bidiagonal form [ MR 1999390 ]
    • Alexander Olshevsky, Vadim Olshevsky and Jun Wang — A comrade-matrix-based derivation of the eight versions of fast cosine and sine transforms [ MR 1999391 ]
    • Dario A. Bini, Luca Gemignani and Beatrice Meini — Solving certain matrix equations by means of Toeplitz computations: algorithms and applications [ MR 1999392 ]
    • Franklin T. Luk and Sanzheng Qiao — A fast singular value algorithm for Hankel matrices [ MR 1999393 ]
    • D. Calvetti, L. Reichel and F. Sgallari — A modified companion matrix method based on Newton polynomials [ MR 1999394 ]
    • Jef Hendrickx, Raf Vandebril and Marc Van Barel — A fast direct method for solving the two-dimensional Helmholtz equation, with Robbins boundary conditions [ MR 1999395 ]
    • Carmine Di Fiore — Structured matrices in unconstrained minimization methods [ MR 1999396 ]
    • Naoharu Ito, Wiland Schmale and Harald K. Wimmer — Computation of minimal state space realizations in Jacobson normal form [ MR 1999397 ]
    • Anita Mayo — High order accurate particular solutions of the biharmonic equation on general regions [ MR 1999398 ]
    • Tong Wen, Alan Edelman and David Gorsich — A fast projected conjugate gradient algorithm for training support vector machines [ MR 1999399 ]
    • V. Olshevsky and M. Amin Shokrollahi — A displacement approach to decoding algebraic codes [ MR 1999400 ]
    • Matthias Bollhöfer and Volker Mehrmann — Some convergence estimates for algebraic multilevel preconditioners [ MR 1999401 ]
    • D. Noutsos, S. Serra Capizzano and P. Vassalos — Spectral equivalence and matrix algebra preconditioners for multilevel Toeplitz systems: a negative result [ MR 1999402 ]
    • William F. Trench — Spectral distribution of Hermitian Toeplitz matrices formally generated by rational functions [ MR 1999403 ]
    • Dario Fasino and Stefano Serra Capizzano — From Toeplitz matrix sequences to zero distribution of orthogonal polynomials [ MR 1999404 ]
    • Kenneth R. Driessel — On Lie algebras, submanifolds and structured matrices [ MR 1999405 ]
    • Harry Dym — Riccati equations and bitangential interpolation problems with singular Pick matrices [ MR 1999406 ]
    • V. Bolotnikov, A. Kheifets and L. Rodman — Functions with Pick matrices having bounded number of negative eigenvalues [ MR 1999407 ]
    • Yu. M. Arlinskiĭ, S. Hassi, H. S. V. de Snoo and E. R. Tsekanovskiĭ — One-dimensional perturbations of selfadjoint operators with finite or discrete spectrum [ MR 1999408 ]
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Contemporary Mathematics
Volume: 323; 2003; 433 pp
MSC: Primary 68; 65; 15; 47

One of the best known fast computational algorithms is the fast Fourier transform method. Its efficiency is based mainly on the special structure of the discrete Fourier transform matrix. Recently, many other algorithms of this type were discovered, and the theory of structured matrices emerged.

This volume contains 22 survey and research papers devoted to a variety of theoretical and practical aspects of the design of fast algorithms for structured matrices and related issues. Included are several papers containing various affirmative and negative results in this direction. The theory of rational interpolation is one of the excellent sources providing intuition and methods to design fast algorithms. The volume contains several computational and theoretical papers on the topic. There are several papers on new applications of structured matrices, e.g., to the design of fast decoding algorithms, computing state-space realizations, relations to Lie algebras, unconstrained optimization, solving matrix equations, etc.

The book is suitable for mathematicians, engineers, and numerical analysts who design, study, and use fast computational algorithms based on the theory of structured matrices.

This volume is a joint publication of the American Mathematical Society and the Society for Industrial and Applied Mathematics.
Readership

Graduate students and research mathematicians interested in the theory and applications of fast numerical algorithms.
  • Articles
  • Vadim Olshevsky — Pivoting for structured matrices and rational tangential interpolation [ MR 1999387 ]
  • Georg Heinig — Inversion of Toeplitz-plus-Hankel matrices with arbitrary rank profile [ MR 1999388 ]
  • Dario Fasino and Luca Gemignani — A Lanczos-type algorithm for the QR factorization of Cauchy-like matrices [ MR 1999389 ]
  • Dario Fasino, Nicola Mastronardi and Marc Van Barel — Fast and stable algorithms for reducing diagonal plus semiseparable matrices to tridiagonal and bidiagonal form [ MR 1999390 ]
  • Alexander Olshevsky, Vadim Olshevsky and Jun Wang — A comrade-matrix-based derivation of the eight versions of fast cosine and sine transforms [ MR 1999391 ]
  • Dario A. Bini, Luca Gemignani and Beatrice Meini — Solving certain matrix equations by means of Toeplitz computations: algorithms and applications [ MR 1999392 ]
  • Franklin T. Luk and Sanzheng Qiao — A fast singular value algorithm for Hankel matrices [ MR 1999393 ]
  • D. Calvetti, L. Reichel and F. Sgallari — A modified companion matrix method based on Newton polynomials [ MR 1999394 ]
  • Jef Hendrickx, Raf Vandebril and Marc Van Barel — A fast direct method for solving the two-dimensional Helmholtz equation, with Robbins boundary conditions [ MR 1999395 ]
  • Carmine Di Fiore — Structured matrices in unconstrained minimization methods [ MR 1999396 ]
  • Naoharu Ito, Wiland Schmale and Harald K. Wimmer — Computation of minimal state space realizations in Jacobson normal form [ MR 1999397 ]
  • Anita Mayo — High order accurate particular solutions of the biharmonic equation on general regions [ MR 1999398 ]
  • Tong Wen, Alan Edelman and David Gorsich — A fast projected conjugate gradient algorithm for training support vector machines [ MR 1999399 ]
  • V. Olshevsky and M. Amin Shokrollahi — A displacement approach to decoding algebraic codes [ MR 1999400 ]
  • Matthias Bollhöfer and Volker Mehrmann — Some convergence estimates for algebraic multilevel preconditioners [ MR 1999401 ]
  • D. Noutsos, S. Serra Capizzano and P. Vassalos — Spectral equivalence and matrix algebra preconditioners for multilevel Toeplitz systems: a negative result [ MR 1999402 ]
  • William F. Trench — Spectral distribution of Hermitian Toeplitz matrices formally generated by rational functions [ MR 1999403 ]
  • Dario Fasino and Stefano Serra Capizzano — From Toeplitz matrix sequences to zero distribution of orthogonal polynomials [ MR 1999404 ]
  • Kenneth R. Driessel — On Lie algebras, submanifolds and structured matrices [ MR 1999405 ]
  • Harry Dym — Riccati equations and bitangential interpolation problems with singular Pick matrices [ MR 1999406 ]
  • V. Bolotnikov, A. Kheifets and L. Rodman — Functions with Pick matrices having bounded number of negative eigenvalues [ MR 1999407 ]
  • Yu. M. Arlinskiĭ, S. Hassi, H. S. V. de Snoo and E. R. Tsekanovskiĭ — One-dimensional perturbations of selfadjoint operators with finite or discrete spectrum [ MR 1999408 ]
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