Fast Algorithms for Structured Matrices : Theory and Applications.
- 1st ed.
- 1 online resource (448 pages)
- Contemporary Mathematics ; v.323 .
- Contemporary Mathematics .
Intro -- Contents -- Foreword -- Pivoting for Structured Matrices and Rational Tangential Interpolation -- Inversion of Toeplitz-Plus-Hankel Matrices with Arbitrary Rank Profile -- A Lanczos-type Algorithm for the QR Factorization of Cauchy-like Matrices -- Fast and Stable Algorithms for Reducing Diagonal Plus Semiseparable Matrices to Tridiagonal and Bidiagonal Form -- A Comrade-Matrix-Based Derivation of the Eight Versions of Fast Cosine and Sine Transforms -- Solving Certain Matrix Equations by Means of Toeplitz Computations: Algorithms and Applications -- A Fast Singular Value Algorithm for Hankel Matrices -- A Modified Companion Matrix Method Based on Newton Polynomials -- A Fast Direct Method for Solving the Two-dimensional Helmholtz Equation, with Robbins Boundary Conditions -- Structured Matrices in Unconstrained Minimization Methods -- Computation of Minimal State Space Realizations in Jacobson Normal Form -- High Order Accurate Particular Solutions of the Biharmonic Equation on General Regions -- A Fast Projected Conjugate Gradient Algorithm for Training Support Vector Machines -- A Displacement Approach to Decoding Algebraic Codes -- Some Convergence Estimates for Algebraic Multilevel Preconditioners -- Spectral Equivalence and Matrix Algebra Preconditioners for Multilevel Toeplitz Systems: A Negative Result -- Spectral Distribution of Hermitian Toeplitz Matrices Formally Generated by Rational Functions -- From Toeplitz Matrix Sequences to Zero Distribution of Orthogonal Polynomials -- On Lie Algebras, Submanifolds and Structured Matrices -- Riccati Equations and Bitangential Interpolation Problems with Singular Pick Matrices -- Functions with Pick Matrices having Bounded Number of Negative Eigenvalues -- One-dimensional Perturbations of Selfadjoint Operators with Finite or Discrete Spectrum.