Additive preconditioning for matrix computations

Authors:
Victor Y. Pan;Dmitriy Ivolgin;Brian Murphy;Rhys Eric Rosholt;Yuqing Tang;Xiaodong Yan
Affiliations:
Department of Mathematics and Computer Science, Lehman College, City University of New York, Bronx, NY;The City University of New York, New York, NY;Department of Mathematics and Computer Science, Lehman College, City University of New York, Bronx, NY;Department of Mathematics and Computer Science, Lehman College, City University of New York, Bronx, NY;The City University of New York, New York, NY;The City University of New York, New York, NY
Venue:
CSR'08 Proceedings of the 3rd international conference on Computer science: theory and applications
Year:
2008

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Abstract

Our weakly random additive preconditioners facilitate the solution of linear systems of equations and other fundamental matrix computations. Compared to the popular SVD-based multiplicative preconditioners, these preconditioners are generated more readily and for a much wider class of input matrices. Furthermore they better preserve matrix structure and sparseness and have a wider range of applications, in particular to linear systems with rectangular coefficient matrices. We study the generation of such preconditioners and their impact on conditioning of the input matrix. Our analysis and experiments show the power of our approach even where we use very weak randomization and choose sparse and/or structured preconditioners.