Structured Matrices and Polynomials

Unified Superfast Algorithms

By: Victor Pan

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Hardcover | 26 June 2001

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Hardcover
308 Pages

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23.5 x 15.88 x 1.91

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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 The book goes beyond research frontiers and, apart from very recent research articles, includes yet unpublished results.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.

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You Can Find This Book In

Non-Fiction Mathematics Algebra Computing & I.T.Computer Programming & Software Development Algorithms & Data Structures Calculus & Mathematical Analysis Numerical Analysis Computer Science Databases Data Capture & Analysis Applied Mathematics

Preface
Glossary of Mathematical Notation
Computations with Structured Matrices: Introduction
Toeplitz/Hankel Matrix Structure and Polynomial Computations
Matrix Structures of Vandermonde and Cauchy Types and Polynomial and Rational Computations
Structured Matrices and Displacement Operators
Unified Superfast Divide-and-Conquer Algorithms for Structured Matrices
Newton-Structured Numerical Iteration
Newton Algebraic Iteration and Newton-Structured Algebraic Iteration
Conclusion
Bibliography
Index
Table of Contents provided by Publisher. All Rights Reserved.

Structured Matrices and Polynomials

Unified Superfast Algorithms

At a Glance

Hardcover

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How to return your order

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