Preconditioning, randomization, solving linear systems, eigen-solving, and root-finding

Authors:
Victor Y. Pan;Guoliang Qian;Ai-Long Zheng
Affiliations:
City University of New York, Bronx, NY, USA;City University of New York, New York, NY, USA;City University of New York, New York, NY, USA
Venue:
Proceedings of the 2009 conference on Symbolic numeric computation
Year:
2009

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Abstract

We propose novel randomized preprocessing techniques for solving linear systems of equations and eigen-solving with extensions to the solution of polynomial and secular equations. According to our formal study and extensive experiments, the approach turns out to be effective, particularly in the case of structured input matrices.