Structured Matrices and Polynomials: Unified Superfast Algorithms - Hardcover

Pan, Victor Y.

Hardcover

ISBN 10: 0817642404 ISBN 13: 9780817642402

Publisher: Birkhäuser, 2001

Synopsis

Structured matrices serve as a natural bridge between the areas of algebraic computations with polynomials and numerical matrix computations, allowing cross-fertilization of both fields. This book covers most fundamental numerical and algebraic computations with Toeplitz, Hankel, Vandermonde, Cauchy, and other popular structured matrices. Throughout the computations, the matrices are represented by their compressed images, called displacements, enabling both a unified treatment of various matrix structures and dramatic saving of computer time and memory. The resulting superfast algorithms allow further dramatic parallel acceleration using FFT and fast sine and cosine transforms. Included are specific applications to other fields, in particular, superfast solutions to: various fundamental problems of computer algebra; the tangential Nevanlinna--Pick and matrix Nehari problems The primary intended readership for this work includes researchers, algorithm designers, and advanced graduate students in the fields of computations with structured matrices, computer algebra, and numerical rational interpolation. The book goes beyond research frontiers and, apart from very recent research articles, includes yet unpublished results. To serve a wider audience, the presentation unfolds systematically and is written in a user-friendly engaging style. Only some preliminary knowledge of the fundamentals of linear algebra is required. This makes the material accessible to graduate students and new researchers who wish to study the rapidly exploding area of computations with structured matrices and polynomials. Examples, tables, figures, exercises, extensive bibliography, and index lend this text to classroom use or self-study.

About this title

Synopsis

This book covers most fundamental numerical and algebraic computations with Toeplitz, Hankel, Vandermonde, Cauchy, and other popular structured matrices. Throughout the computations, the matrices are represented by their compressed images, called displacements, enabling both a unified treatment of various matrix structures and dramatic saving of computer time and memory. The resulting superfast algorithms allow further dramatic parallel acceleration using FFT. Included are specific applications to other fields, in particular, superfast solutions to: various fundamental problems of computer algebra * the tangential Nevanlinna-Pick and matrix Nehari problems * loss-resilient encoding/decoding problems. The primary intended readership includes researchers, algorithm designers, and advanced graduate students in the fields of computations with structured matrices, computer algebra, and numerical rational interpolation. The book goes beyond research frontiers and, apart from very recent research articles, includes yet unpublished results. To serve a wider audience, the presentation unfolds systematically and is written in a user-friendly engaging style.

Only some preliminary knowledge of the fundamentals of linear algebra is required. This makes the material accessible to novices who wish to study the rapidly exploding area of computations with structured matrices and polynomials. Examples, tables, figures, exercises, and an extensive bibliography lend this text to classroom use or self-study.

Edition details

• Publisher: Birkhäuser
• Publication date: 2001
• Language: English
• ISBN 10: 0817642404
• ISBN 13: 9780817642402
• Binding: Hardcover
• Number of pages: 303