Some Properties of the Optimal Preconditioner and the Generalized Superoptimal Preconditioner

Some Properties of the Optimal Preconditioner and the Generalized Superoptimal Preconditioner

Year:    2010

Numerical Mathematics: Theory, Methods and Applications, Vol. 3 (2010), Iss. 4 : pp. 449–460

Abstract

The optimal preconditioner and the superoptimal preconditioner were proposed in 1988 and 1992 respectively. They have been studied widely since then. Recently, Chen and Jin [6] extend the superoptimal preconditioner to a more general case by using the Moore-Penrose inverse. In this paper, we further study some useful properties of the optimal and the generalized superoptimal preconditioners. Several existing results are extended and new properties are developed.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/nmtma.2010.m9013

Numerical Mathematics: Theory, Methods and Applications, Vol. 3 (2010), Iss. 4 : pp. 449–460

Published online:    2010-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    12

Keywords:    Optimal preconditioner generalized superoptimal preconditioner Moore-Penrose inverse unitarily invariant norm semi-stability singular value.

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