Abstract

. We present and compare several methods for multiplying banded square matrices. Various storage schemes and their implementations are discussed. Of particular interest is an algorithm for multiplying matrices by diagonals, which always references contiguous matrix elements. Two blocked implementations also are presented. These specialized routines are attractive for multiplying matrices whose bandwidths are known to be small relative to the size of the matrices. Results from tests performed on a Cray-2, Cray Y-MP, and RS/6000 are given. It is shown that, for specialized applications, a substantial savings can be realized over the standard three-loop multiplication algorithm. 1. Motivation During the development of the Invariant Subspace Decomposition Algorithm (ISDA) [3], which computes the eigenvalues and eigenvectors of matrices, we began an investigation into the issues relating to banded matrices. In particular, since the ISDA relies heavily on matrix multiplication to decompose ...

Citations