Some Properties of the Optimal Preconditioner and the Generalized Superoptimal Preconditioner
DOI:
https://doi.org/10.4208/nmtma.2010.m9013Keywords:
Optimal preconditioner, generalized superoptimal preconditioner, Moore-Penrose inverse, unitarily invariant norm, semi-stability, singular value.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.