Parallelizing a Code for Counting and Computing Eigenvalues of Complex Tridiagonal Matrices and Roots of Complex Polynomials

Vassilis Geroyannis, Florendia Valvi

Department of Mathematics, University of Patras, Patras, Greece.
Department of Physics, University of Patras, Patras, Greece.

DOI: 10.4236/am.2013.45109                

Abstract

A code developed recently by the authors, for counting and computing the eigenvalues of a complex tridiagonal matrix, as well as the roots of a complex polynomial, which lie in a given region of the complex plane, is modified to run in parallel on multi-core machines. A basic characteristic of this code (eventually pointing to its parallelization) is that it can proceed with: 1) partitioning the given region into an appropriate number of subregions; 2) counting eigenvalues in each subregion; and 3) computing (already counted) eigenvalues in each subregion. Consequently, theoretically speaking, the whole code in itself parallelizes ideally. We carry out several numerical experiments with random complex tridiagonal matrices, and random complex polynomials as well, in order to study the behaviour of the parallel code, especially the degree of declination from theoretical expectations.

Keywords

Complex Polynomial; Complex Tridiagonal Matrix; Eigenvalues; Numerical Methods; OpenMP; Parallel Code; Parallel Programming

Conflicts of Interest

The authors declare no conflicts of interest.

References

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