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