Linear algebra, rational approximation, and orthogonal polynomials

Adhemar Bultheel and Marc Van Barel (Eds.)9780080535524, 9780444828729, 0444828729

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.

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Table of contents :
Content:
Preface
Pages v-x

List of Symbols
Pages xv-xvii

Chapter 1 Euclidean fugues Original Research Article
Pages 1-59

Chapter 2 Linear algebra of Hankels Original Research Article
Pages 61-98

Chapter 3 Lanczos algorithm Original Research Article
Pages 99-133

Chapter 4 Orthogonal polynomials Original Research Article
Pages 135-229

Chapter 5 Padé approximation Original Research Article
Pages 231-270

Chapter 6 Linear systems and partial realization Original Research Article
Pages 271-349

Chapter 7 General rational interpolation Original Research Article
Pages 351-383

Chapter 8 Wavelets and the lifting scheme Original Research Article
Pages 385-411

Bibliography
Pages 413-433

List of algorithms
Page 435

Index
Pages 436-446