On the Automatic Scaling of Matrices for Gaussian Elimination

Abstract

The usual pivotal strategies for Gaussian elimination are based on the assumption that all the matrix elements are of comparable size. We propose an algorithm for scaling based on the assumption that the given matrix can be scaled to this required form. Some numerical experiments are presented to show that it produces much better results than straightforward row and column norm equilibration, particularly in the sparse case, and that the computing cost is moderate.