Numerical Methods for Structured Matrices and Applications: The Georg Heinig Memorial Volume

ISBN-13: 9783764389956 / Angielski / Twarda / 2010 / 439 str.

Dario Andrea Bini; Volker Mehrmann; Vadim Olshevsky

Opis

This cross-disciplinary volume brings together theoretical mathematicians, engineers and numerical analysts and publishes surveys and research articles related to the topics where Georg Heinig had made outstanding achievements. In particular, this includes contributions from the fields of structured matrices, fast algorithms, operator theory, and applications to system theory and signal processing.

Spis treści

Georg Heinig.- Georg Heinig (1947—2005) In Memoriam.- Georg Heinig November 24, 1947 - May 10, 2005 A Personal Memoir and Appreciation.- to Bezoutians.- On Matrices that are not Similar to a Toeplitz Matrix and a Family of Polynomials Tewodros Amdeberhan and Georg Heinig.- Research Contributions.- A Traub-like Algorithm for Hessenbergquasiseparable- Vandermonde Matrices of Arbitrary Order.- A Fast Algorithm for Approximate Polynomial GCD Based on Structured Matrix Computations.- On Inertia of Some Structured Hermitian Matrices.- Variable-coefficient Toeplitz Matrices with Symbols beyond the Wiener Algebra.- A Priori Estimates on the Structured Conditioning of Cauchy and Vandermonde Matrices.- Factorizations of Totally Negative Matrices.- QR-factorization of Displacement Structured Matrices Using a Rank Structured Matrix Approach.- Bezoutians Applied to Least Squares Approximation of Rational Functions.- On the Weyl Matrix Balls Corresponding to the Matricial Carathéodory Problem in Both Nondegenerate and Degenerate Cases.- On Extremal Problems of Interpolation Theory with Unique Solution.- O(n) Algorithms for Banded Plus Semiseparable Matrices.- Unified Nearly Optimal Algorithms for Structured Integer Matrices.- V-cycle Optimal Convergence for DCT-III Matrices.- The Ratio Between the Toeplitz and the Unstructured Condition Number.- A New Algorithm for Finding Positive Eigenvectors for a Class of Nonlinear Operators Associated with M-matrices.- Hankel Minors and Pade Approximations.