الگوریتم‌های سریع برای ماتریس‌های ساختاری: نظریه و کاربردها

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. 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.--book Jacket. Pivoting For Structured Matrices And Rational Tangential Interpolation / Vadim Olshevsky -- Inversion Of Toeplitz-plus-hankel Matrices With Arbitrary Rank Profile / Georg Heinig -- Lanczos-type Algorithm For The Qr Factorization Of Cauchy-like Matrices / Dario Fasino And Luca Gemignani -- Fast And Stable Algorithms For Reducing Diagonal Plus Semiseparable Matrices To Tridiagonal And Bidiagonal Form / Dario Fasino, Nicola Mastronardi And Marc Van Barel -- Comrade-matrix-based Derivation Of The Eight Versions Of Fast Cosine And Sine Transforms / Alexander Olshevsky, Vadim Olshevsky And Jun Wang -- Solving Certain Matrix Equations By Means Of Toeplitz Computations: Algorithms And Applications / Dario A. Bini, Luca Gemignani And Beatrice Meini -- Fast Singular Value Algorithm For Hankel Matrices / Franklin T. Luk And Sanzheng Qiao -- Modified Companion Matrix Method Based On Newton Polynomials / D. Calvetti, L. Reichel And F. Sgallari -- Fast Direct Method For Solving The Two-dimensional Helmholtz Equation, With Robbins Boundary Conditions / J. Hendrickx, Raf Vandebril And Marc Van Barel -- Structured Matrices In Unconstrained Minimization Methods / Carmine Di Fiore -- Computation Of Minimal State Space Realizations In Jacobson Normal Form / Naoharu Ito, Wiland Schmale And Harald K. Wimmer -- High Order Accurate Particular Solutions Of The Biharmonic Equation On General Regions / Anita Mayo -- Fast Projected Conjugate Gradient Algorithm For Training Support Vector Machines / Tong Wen, Alan Edelman And David Gorsich -- Displacement Approach To Decoding Algebraic Codes / V. Olshevsky And M. Amin Shokrollahi -- Some Convergence Estimates For Algebraic Multilevel Preconditoners / Matthias Bollhofer And Volker Mehrmann Spectral Equivalence And Matrix Algebra Preconditioners For Multilevel Toeplitz Systems: A Negative Result / D. Noutsos, S. Serra Capizzano And R. Vassalos -- Spectral Distribution Of Hermitian Toeplitz Matrices Formally Generated By Rational Functions / William F. Trench -- From Toeplitz Matrix Sequences To Zero Distribution Of Orthogonal Polynomials / Dario Fasino And Stefano Serra Capizzano -- On Lie Algebras, Submanifolds And Structured Matrices / Kenneth R. Driessel -- Riccati Equations And Bitangential Interpolation Problems With Singular Pick Matrices / Harry Dym -- Functions With Pick Matrices Having Bounded Number Of Negative Eigenvalues / V. Bolotnikov, A. Kheifets And L. Rodman -- One-dimensional Perturbations Of Selfadjoint Operators With Finite Or Discrete Spectrum / Yu. M. Arlinskii, S. Hassi, H. S. V. De Snoo And E. R. Tsekanovskii. Vadim Olshevsky, Editor. Includes Bibliographical References.