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 biconju-
gate 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.