The symmetric-toeplitz linear system problem in parallel

Abstract

Many algorithms exist that exploit the special structure of Toeplitz matrices for solving linear systems. Nevertheless, these algorithms are difficult to parallelize due to its lower computational cost and the great dependency of the operations involved that produces a great communication cost. The foundation of the parallel algorithm presented in this paper consists of transforming the Toeplitz matrix into a another structured matrix called Cauchy-like. The particular properties of Cauchy-like matrices are exploited in order to obtain two levels of parallelism that makes possible to highly reduce the execution time. The experimental results were obtained in a cluster of PC's. © Springer-Verlag Berlin Heidelberg 2005.