Iterative refinement of solution with biparameter for solving ill-conditioned systems of linear algebraic equations

摘要

Although the idea of iteration refinement for improving the computed solution to a system of linear equations can go back to 1948, the technique has remained popular [SIAM, Philadelphia, PA, 1998; BIT 17 (1977) 303; Math. Comput. 35 (1980) 817; J. Numer. Anal. 17(4) (1997) 495]. In this paper, a new iterative improvement of solution with biparameter for solving ill-conditioned systems of linear algebraic equations is proposed. Both theoretical convergence analysis and numerical experiments are presented to show the efficiency and accuracy of our method.