Erin Carson and James Demmel

EECS Department, University of California, Berkeley

Technical Report No. UCB/EECS-2014-18

March 13, 2014

http://www2.eecs.berkeley.edu/Pubs/TechRpts/2014/EECS-2014-18.pdf

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.

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BibTeX citation:

@techreport{Carson:EECS-2014-18,
    Author= {Carson, Erin and Demmel, James},
    Title= {Analysis of the finite precision s-step biconjugate gradient method},
    Year= {2014},
    Month= {Mar},
    Url= {http://www2.eecs.berkeley.edu/Pubs/TechRpts/2014/EECS-2014-18.html},
    Number= {UCB/EECS-2014-18},
    Abstract= {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.},
}

EndNote citation:

%0 Report
%A Carson, Erin 
%A Demmel, James 
%T Analysis of the finite precision s-step biconjugate gradient method
%I EECS Department, University of California, Berkeley
%D 2014
%8 March 13
%@ UCB/EECS-2014-18
%U http://www2.eecs.berkeley.edu/Pubs/TechRpts/2014/EECS-2014-18.html
%F Carson:EECS-2014-18