A Sparse QS-Decomposition for Large Sparse Linear System of Equations

Abstract

A direct solver for large scale sparse linear system of equations is presented in this paper. As a direct solver, this method is among the most efficient direct solvers available so far with flop count as \(O(n\, log n)\) in one-dimensional situations and \(O(n^{3/2}) \) in second dimensional situation. This method has advantages over the existing fast solvers in which it can be used to handle more general situations, both well-conditioned or ill-conditioned systems; more importantly, it is a very stable solver and a naturally parallel procedure! Numerical experiments are presented to demonstrate the efficiency and stability of this algorithm.