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

摘要

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 logn) 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.