Vectors and matrices are useful in representing multivariate numeric data, and they occur
naturally in working with linear equations or when expressing linear relationships among …

We survey general techniques and open problems in numerical linear algebra on parallel
architectures. We first discuss basic principles of paralled processing, describing the costs of …

The computation of the singular value decomposition, or SVD, has a long history with many
improvements over the years, both in its implementations and algorithmically. Here, we …

A variation of Paige's algorithm is presented for computing the generalized singular value
decomposition (GSVD) of two matrices A and B. There are two innovations. The first is a new …

A very fast Jacobi-like algorithm for the parallel solution of symmetric eigenvalue problems is
proposed. It becomes possible by not focusing on the realization of the Jacobi rotation with a …

The authors consider two parallel Jacobi algorithms, due to RP Brent et al.(J. VLSI Comput.
Syst., vol. 1, p. 242-70, 1985) and FT Luk (1986 J. Lin. Alg. Applic., vol. 77, p. 259-73), for …

Publisher Summary This chapter explains some matrix computations that are common in
statistics. Most of these techniques also arise in other applications, including the solution of …

Since the CS decomposition (CSD) and the generalized singular value decomposition
(GSVD) emerged as the generalization of the singular value decomposition about fifteen …

Abstract................................................................................. 118 4.1 Introduction..................................
...................................... 1184.1. 1 Basics...................................................................... 118 4.1. 2 …

Five variants of a new dynamic ordering are presented for the parallel one-sided block
Jacobi SVD algorithm. Similarly to the two-sided algorithm, the dynamic ordering takes into …