Rehabilitation of the Gauss-Jordan algorithm
By using vector and parallel computers, a number of algorithms may have a renewed interest. In this paper, the Gauss-Jordan algorithm with column interchanges is analyzed. It is shown that by using the Gauss-Jordan algorithm with column interchanges, a more satisfactory bound for the residual norm can be given. The presented error analysis gives a theoretical evidence that this algorithm yields numerical solutions as good as those obtained by Gauss elimination. Furthermore, the residual of the obtained solution is not larger than that corresponding to the Gauss elimination's solution. For demonstrating that the error and the residual are satisfactory, some computer results are presented. Some results of experiments on a Cyber 205 vector computer are gathered to show that the Gauss-Jordan algorithm is not slower than the Gauss elimination for systems of order up to 25, although for its realization, about 1,5 times work is required.
scientific article; zbMATH DE number 4100478