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Application of the Parallel Dichotomy Algorithm for solving Toeplitz tridiagonal systems of linear equations with one right-hand side
Basing on a modification of the "Dichotomy Algorithm" (Terekhov, 2010), we
propose a parallel procedure for solving tridiagonal systems of equations with
Toeplitz matrices. Taking the structure of the Toeplitz matrices, we may
substantially reduce the number of the "preliminary calculations" of the
Dichotomy Algorithm, which makes it possible to effectively solve a series as
well as a single system of equations. On the example of solving of elliptic
equations by the Separation Variable Method, we show that the computation
accuracy is comparable with the sequential version of the Thomas method, and
the dependence of the speedup on the number of processors is almost linear. The
proposed modification is aimed at parallel realization of a broad class of
numerical methods including the inversion of Toeplitz and quasi-Toeplitz
tridiagonal matrices.Comment: New tests have been adde