The stable parallel solution of general narrow banded linear systems

Abstract

We propose a stable algorithm for the parallel solution of banded and periodically banded linear systems. While most of the known parallel algorithms are stable only for symmetric positive definite or diagonally dominant systems, the new algorithm incorporates pivoting without sacrificing efficiency. The principle ingredient of the algorithm is a bidiagonal cyclic reduction that admits pivoting. We report on numerical experiments conducted on various multiprocessor computers.