Structured Matrices and Polynomials

Unified Superfast Algorithms
2001
ISBN: 978-0-8176-4240-2
Verlag: Birkhäuser Boston

Buch, Englisch, 278 Seiten, HC runder Rücken kaschiert, Format (B × H): 160 mm x 241 mm, Gewicht: 1350 g

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unpublished results.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.

Zielgruppe

Research

Autoren/Hrsg.

Pan, Victor Y.

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Lineare und multilineare Algebra, Matrizentheorie
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Numerische Mathematik
• Mathematik | Informatik EDV | Informatik Informatik
• Mathematik | Informatik Mathematik Algebra Homologische Algebra

Inhaltsverzeichnis

Preface * Glossary of Mathematical Notation * 1. Computations with
Structured Matrices: Introduction * 2. Toeplitz/Hankel Matrix
Structure and Polynomial Computations * 3. Matrix Structures of
Vandermonde and Cauchy Types and Polynomial and Rational Computations
* 4. Structured Matrices and Displacement Operators * 5. Unified
Superfast Divide-and-Conquer Algorithms for Structured Matrices * 6.
Newton-Structured Numerical Iteration * 7. Newton Algebraic Iteration
and Newton-Structured Algebraic Iteration * Conclusion * Bibliography
* Index