Fast Algorithms for Structured Matrices
Theory and Applications
Published on 15. May 2003
Book
Paperback/Softback
448 pages
978-0-8218-3177-9 (ISBN)
Description
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 in this title 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.
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.
More details
Series
Edition
New ed.
Language
English
Place of publication
Providence
United States
Target group
Professional and scholarly
Dimensions
Height: 200 mm
Weight
780 gr
ISBN-13
978-0-8218-3177-9 (9780821831779)
Copyright in bibliographic data is held by Nielsen Book Services Limited or its licensors: all rights reserved.
Schweitzer Classification
Person
Olshevsky, Vadim (University of Connecticut, Storrs, USA)
Content
Pivoting for structured matrices and rational tangential interpolation by V. Olshevsky Inversion of Toeplitz-plus-Hankel matrices with arbitrary rank profile by G. Heinig A Lanczos-type algorithm for the QR factorization of Cauchy-like matrices by D. Fasino and L. Gemignani Fast and stable algorithms for reducing diagonal plus semiseparable matrices to tridiagonal and bidiagonal form by D. Fasino, N. Mastronardi, and M. Van Barel A comrade-matrix-based derivation of the eight versions of fast cosine and sine transforms by A. Olshevsky, V. Olshevsky, and J. Wang Solving certain matrix equations by means of Toeplitz computations: algorithms and applications by D. A. Bini, L. Gemignani, and B. Meini A fast singular value algorithm for Hankel matrices by F. T. Luk and S. Qiao A modified companion matrix method based on Newton polynomials by D. Calvetti, L. Reichel, and F. Sgallari A fast direct method for solving the two-dimensional Helmholtz equation, with Robbins boundary conditions by J. Hendrickx, R. Vandebril, and M. Van Barel Structured matrices in unconstrained minimization methods by C. Di Fiore Computation of minimal state space realizations in Jacobson normal form by N. Ito, W. Schmale, and H. K. Wimmer High order accurate particular solutions of the biharmonic equation on general regions by A. Mayo A fast projected conjugate gradient algorithm for training support vector machines by T. Wen, A. Edelman, and D. Gorsich A displacement approach to decoding algebraic codes by V. Olshevsky and M. A. Shokrollahi Some convergence estimates for algebraic multilevel preconditioners by M. Bollhofer and V. Mehrmann Spectral equivalence and matrix algebra preconditioners for multilevel Toeplitz systems: a negative result by D. Noutsos, S. S. Capizzano, and P. Vassalos Spectral distribution of Hermitian Toeplitz matrices formally generated by rational functions by W. F. Trench From Toeplitz matrix sequences to zero distribution of orthogonal polynomials by D. Fasino and S. S. Capizzano On Lie algebras, submanifolds and structured matrices by K. R. Driessel Riccati equations and bitangential interpolation problems with singular Pick matrices by H. Dym Functions with Pick matrices having bounded number of negative eigenvalues by V. Bolotnikov, A. Kheifets, and L. Rodman One-dimensional perturbations of selfadjoint operators with finite or discrete spectrum by Yu. M. Arlinskii, S. Hassi, H. S. V. de Snoo, and E. R. Tsekanovskii.