A PARALLEL ALGORITHM FOR THE MATRIX SIGN FUNCTION

Abstract

We propose a new parallel algorithm for computing the sign function of a matrix. The algorithm is based on the Padé approximation of a certain hypergeometric function which in turn leads to a rational function approximation to the sign function. Parallelism is achieved by developing a partial fraction expansion of the rational function approximation since each fraction can be evaluated on a separate processor in parallel. For the sign function the partial fraction expansion is numerically attractive since the roots and the weights are known analytically and can be computed very accurately. We also present experimental results obtained on a Cray Y-MP.