A multilevel parallel algorithm to solve symmetric Toeplitz linear systems

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Abstract

This paper presents a parallel algorithm to solve a structured linear system with a symmetric-Toeplitz matrix. Our main result concerns the use of a combination of shared and distributed memory programming tools to obtain a multilevel algorithm that exploits the actual different hierarchical levels of memory and computational units present in parallel architectures. This gives, as a result, a so-called parallel hybrid algorithm that is able to exploit each of these different configurations. Our approach has been done not only by means of combining standard implementation tools like OpenMP and MPI, but performing the appropriate mathematical derivation that allows this derivation. The experimental results over different representations of available parallel hardware configurations show the usefulness of our proposal.

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