Structured Matrices and Polynomials

This book covers fundamental numerical and algebraic computations with Toeplitz, Hankel, Vandermonde, Cauchy, and other popular structured matrices. In the computations, matrices are represented by their compressed images, called displacements, enabling both a unified treatment of various matrix structures and a dramatic saving of computer time and memory. The resulting superfast algorithms allow further dramatic parallel acceleration using FFT. Intended readers: researchers, algorithm designers, advanced grads in the areas of computations with structured matrices, computer algebra, and numerical rational interpolation.

Inhalt
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