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

✍ Scribed by Albrecht Böttcher, Israel Gohberg, Bernd Silbermann (auth.), Dario Andrea Bini, Volker Mehrmann, Vadim Olshevsky, Eugene E. Tyrtyshnikov, Marc van Barel (eds.)

Publisher: Birkhäuser Basel
Year: 2010
Tongue: English
Leaves: 438
Series: Operator Theory: Advances and Applications 199
Edition: 1
Category: Library

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✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-viii
Front Matter....Pages 1-1
Georg Heinig (1947—2005) In Memoriam....Pages 3-6
Georg Heinig November 24, 1947 - May 10, 2005 A Personal Memoir and Appreciation....Pages 7-23
Introduction to Bezoutians....Pages 25-118
On Matrices that are not Similar to a Toeplitz Matrix and a Family of Polynomials Tewodros Amdeberhan and Georg Heinig....Pages 119-123
Front Matter....Pages 125-125
A Traub-like Algorithm for Hessenbergquasiseparable- Vandermonde Matrices of Arbitrary Order....Pages 127-154
A Fast Algorithm for Approximate Polynomial GCD Based on Structured Matrix Computations....Pages 155-173
On Inertia of Some Structured Hermitian Matrices....Pages 175-189
Variable-coefficient Toeplitz Matrices with Symbols beyond the Wiener Algebra....Pages 191-202
A Priori Estimates on the Structured Conditioning of Cauchy and Vandermonde Matrices....Pages 203-220
Factorizations of Totally Negative Matrices....Pages 221-227
QR-factorization of Displacement Structured Matrices Using a Rank Structured Matrix Approach....Pages 229-254
Bezoutians Applied to Least Squares Approximation of Rational Functions....Pages 255-288
On the Weyl Matrix Balls Corresponding to the Matricial Carathéodory Problem in Both Nondegenerate and Degenerate Cases....Pages 289-332
On Extremal Problems of Interpolation Theory with Unique Solution....Pages 333-346
O(n) Algorithms for Banded Plus Semiseparable Matrices....Pages 347-358
Unified Nearly Optimal Algorithms for Structured Integer Matrices....Pages 359-375
V-cycle Optimal Convergence for DCT-III Matrices....Pages 377-396
The Ratio Between the Toeplitz and the Unstructured Condition Number....Pages 397-419
A New Algorithm for Finding Positive Eigenvectors for a Class of Nonlinear Operators Associated with M-matrices....Pages 421-430
Hankel Minors and Pade Approximations....Pages 431-439

✦ Subjects

Numerical Analysis; Operator Theory; Functional Analysis

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