A Parallel Algorithm for Circulant Tridiagonal Linear Systems

Abstract

In this paper, we propose a parallel algorithm for solving the tridiagonal systems, the circulant tridiagonal systems, the block-tridiagonal systems, the circulant block-tridiagonal systems and the banded systems, which is an improvement of Agui’s and Chung’s algorithms. Our algorithm is based on the divide-and-conquer strategy and is suitable for implementation on the hypercube or the binary tree. The applications of our algorithm include solving partial differential equations, the closed B-spline curve fitting problem, the dominant eigenvalues of a matrix and many other scientific, physical and engineering problems.