Reconsideration of Residual Smoothing Technique for Improving the Accuracy of Approximate Solutions of CGS-type Iterative Methods

Abstract

Abstract. Conjugate gradient squared (CGS)-type methods for solving nonsymmetric linear systems often have large oscillations in the residual norms, and they are known to affect the maximum attainable accuracy of approximate solutions. The oscillations may be reduced by using a residual smoothing technique. However, when using the existing implementations, the attainable accuracy of the smoothed sequences is not higher than that of the primary ones. In this paper, we propose an alternative implementation of the smoothing technique to avoid severe propagation of rounding errors, which towards to improve the attainable accuracy. Numerical experiments show the effectiveness of our proposed method.