Schur aggregation for linear systems and determinants

Authors:
V. Y. Pan;D. Grady;B. Murphy;G. Qian;R. E. Rosholt;A. D. Ruslanov
Affiliations:
Department of Mathematics and Computer Science, Lehman College, City University of New York, Bronx, NY 10468, USA;Department of Computer and Information Sciences, State University of New York, Fredonia, NY 14063, USA;Department of Mathematics and Computer Science, Lehman College, City University of New York, Bronx, NY 10468, USA;Ph.D. Program in Computer Science, City University of New York, New York, NY 10036, USA;Department of Mathematics and Computer Science, Lehman College, City University of New York, Bronx, NY 10468, USA;Department of Computer and Information Sciences, State University of New York, Fredonia, NY 14063, USA
Venue:
Theoretical Computer Science
Year:
2008

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Abstract

We apply our recent preconditioning techniques to the solution of linear systems of equations and computing determinants. We combine these techniques with the Sherman-Morrison-Woodbury formula, its new variations, aggregation, iterative refinement, and advanced algorithms that rapidly compute sums and products either error-free or with the desired high accuracy. Our theoretical and experimental study shows the power of this approach.