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.