Structured Matrices and Polynomials

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 The book goes beyond research §frontiers and, apart from very recent research articles, includes yet §unpublished results.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