This handbook provides an up-to-date compendium of fundamental computer science
topics, techniques, and applications. Along with updating and revising many of the existing …

Semiseparable matrices and many other rank‐structured matrices have been widely used in
developing new fast matrix algorithms. In this paper, we generalize the hierarchically …

In recent years several new classes of matrices have been discovered and their structure
exploited to design fast and accurate algorithms. In this new reference work, Raf Vandebril …

We present an algorithm for the solution of polynomial equations and secular equations of
the form S (x)= 0 for S (x)=∑ i= 1 naix− bi− 1= 0, which provides guaranteed approximation …

Our interest in structured matrices was inspired by the outstanding mathematician Professor
Israel Gohberg, our older friend, colleague and teacher. His ideas, projects and our joint …

Given a symmetric positive definite matrix A, we compute a structured approximate Cholesky
factorization A≈R^TR up to any desired accuracy, where R is an upper triangular …

The nonlinear Fourier transform (NFT; also: direct scattering transform) is discussed with
respect to the focusing nonlinear Schrödinger equation on the infinite line. It is shown that …

For dense symmetric matrices with small off-diagonal (numerical) ranks and in a
hierarchically semiseparable form, we give a divide-and-conquer eigendecomposition …

Fifty years after the invention of the QR algorithm by John Francis and Vera Kublanovskaya
we reconstruct the ideas and the influences that led to its genesis from the originators' own …

Matrix methods are increasingly popular for polynomial root-finding. The idea is to
approximate the roots as the eigenvalues of the companion or generalized companion …