Analysis of the Finite Precision s-Step Biconjugate Gradient Method

: We analyze the s-step biconjugate gradient algorithm in nite precision arithmetic and derive a bound for the residual norm in terms of a minimum polynomial of a perturbed matrix multiplied by an ampli cation factor. Our bound enables comparison of s-step and classical biconjugate gradient in terms of ampli cation factors. Our results show that for s-step biconjugate gradient the ampli cation factor depends heavily on the quality of s-step polynomial bases generated in each outer loop.