Variations on the Gram-Schmidt and the Huang algorithms for linear systems: A numerical study

Abstract

In this paper we compare the numerical performance on a set of ill conditioned problems of several algorithms for linear systems based upon the explicit QR factorization and the implicit LQ factorization associated with the Huang and the modified Huang algorithms in the ABS class. The results indicate that the modified Huang algorithm is generally more accurate than the Huang algorithm and competitive with commercial codes based upon the QR factorization with Householder of Givens reflections. The best version of the modified Huang algorithm performs similarly, as theoretically expected, to the doubly iterated Gram-Schmidt method of Daniel et al., applied on the rows to generate search vectors.