Numer. Math. Theor. Meth. Appl., 3 (2010), pp. 449-460.
Published online: 2010-03
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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} }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.