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Volume 3, Issue 4
Some Properties of the Optimal Preconditioner and the Generalized Superoptimal Preconditioner

Hong-Kui Pang & Xiao-Qing Jin

DOI: 10.4208/nmtma.2010.m9013

Numer. Math. Theor. Meth. Appl., 3 (2010), pp. 449-460.

Published online: 2010-03

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  • 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.

  • Keywords

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

  • AMS Subject Headings

65F10, 65F15, 65F35, 65F99

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-3-449, author = {}, title = {Some Properties of the Optimal Preconditioner and the Generalized Superoptimal Preconditioner}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2010}, volume = {3}, number = {4}, pages = {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.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2010.m9013}, url = {http://global-sci.org/intro/article_detail/nmtma/6008.html} }
TY - JOUR T1 - Some Properties of the Optimal Preconditioner and the Generalized Superoptimal Preconditioner JO - Numerical Mathematics: Theory, Methods and Applications VL - 4 SP - 449 EP - 460 PY - 2010 DA - 2010/03 SN - 3 DO - http://doi.org/10.4208/nmtma.2010.m9013 UR - https://global-sci.org/intro/article_detail/nmtma/6008.html KW - Optimal preconditioner, generalized superoptimal preconditioner, Moore-Penrose inverse, unitarily invariant norm, semi-stability, singular value. AB -

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.

Hong-Kui Pang & Xiao-Qing Jin. (2020). Some Properties of the Optimal Preconditioner and the Generalized Superoptimal Preconditioner. Numerical Mathematics: Theory, Methods and Applications. 3 (4). 449-460. doi:10.4208/nmtma.2010.m9013
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