Linear Algebra, Rational Approximation Orthogonal Polynomials

✍ Scribed by A. Bultheel, M. Van Barel

• Publisher: North-Holland Publishing Co
• Year: 1997
• Tongue: English
• Leaves: 458
• Series: Studies in Computational Mathematics 6
• Edition: illustrated edition
• Category: Library

✦ Synopsis

Evolving from an elementary discussion, this book develops the Euclidean algorithm to a very powerful tool to deal with general continued fractions, non-normal Padé tables, look-ahead algorithms for Hankel and Toeplitz matrices, and for Krylov subspace methods. It introduces the basics of fast algorithms for structured problems and shows how they deal with singular situations.

Links are made with more applied subjects such as linear system theory and signal processing, and with more advanced topics and recent results such as general bi-orthogonal polynomials, minimal Padé approximation, polynomial root location problems in the complex plane, very general rational interpolation problems, and the lifting scheme for wavelet transform computation. The text serves as a supplement to existing books on structured linear algebra problems, rational approximation and orthogonal polynomials.

Features of this book:

• provides a unifying approach to linear algebra, rational approximation and orthogonal polynomials

• requires an elementary knowledge of calculus and linear algebra yet introduces advanced topics.

The book will be of interest to applied mathematicians and engineers and to students and researchers.

✦ Table of Contents

Cover......Page 1
Preface......Page 6
Table of Contents......Page 12
List of Symbols......Page 16
1 Euclidean fugues......Page 20
2 Linear algebra o f Hankels......Page 79
3 Lanczos algorithm......Page 117
4 Orthogonal polynomials......Page 152
5 Pade approximation......Page 247
6 Linear systems......Page 287
7 General rational interpolation......Page 366
8 Wavelets......Page 399
Bibliography......Page 426
List of Algorithms......Page 447
Index......Page 448