NII Technical Report (NII-2008-002E)

Title Generalized Approximate Inverse Preconditioners for Least Squares Problems
Authors Xiaoke Cui, Ken Hayami
Abstract This paper is concerned with a new approach for preconditioning large sparse least squares problems. Based on the idea of the approximate inverse preconditioner, which was originally developed for square matrices, we construct a Generalized Approximate Inverse(GAINV) $M$ which approximately minimizes $\|I-MA\|_F$ or $\|I-AM\|_F$. Then, we also discuss the theoretical issues such as the equivalence between the original least squares problem and the preconditioned problem. Finally, numerical experiments on problems form Matrix Market collection and random matrices show that although the preconditioning is expensive, it pays off in certain cases.
Language English
Published Feb 22, 2008
Pages 13p

NII Technical Reports
National Institute of Informatics