Our Subjects and Objectives. This book is about algebraic and symbolic computation and numerical computing (with matrices and polynomials). It greatly extends the study of these topics presented in the celebrated books of the seventies, AHU] and BM] (these topics have been under-represented in CLR], which is a highly successful extension and updating of AHU] otherwise). Compared to AHU] and BM] our volume adds extensive material on parallel com- putations with general matrices and polynomials, on the bit-complexity of arithmetic computations (including some recent techniques of data...

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...