Handbook of Parallel Computing and Statistics by E. J. Kontoghiorghes (ed.)

Abstract

The goal of the survey is to review the state-of-the-art of computing the Singular Value Decompo sition (SVD) of dense and sparse matrices, with some emphasis on those schemes that are suitabl for parallel computing platforms. For dense matrices, we present those schemes that yield the com plete decomposition, whereas for sparse matrices we describe schemes that yield only the extrema singular triplets. Special attention is devoted to the computation of the smallest singular value which are normally the most difficult to evaluate but which provide a measure of the distance to singularity of the matrix under consideration. Also, we conclude with the presentation of a paralle method for computing pseudospectra, which depends on computing the smallest singular values.