NII Technical Report (NII-2008-008E)

Title Greville's Method for Preconditioning Least Squares Problems
Authors Xiaoke Cui, Ken Hayami
Abstract In this paper, we construct a preconditioner for least squares problems min||b-Ax||, where A can be matrices with any shape and any rank. The preconditioner itself is a sparse approximation to the Moore-Penrose inverse of the coefficient matrix A. For this preconditioner, we give theoretical analysis to show that under certain assumption, the problem preconditioned by this preconditioner is equivalent to the original problem, and the GMRES method can determine a solution to the preconditioned problem before breakdown happens.
Language English
Published Aug 21, 2008
Pages 26p
PDF File 08-008E.pdf

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National Institute of Informatics