Some Properties of the Optimal Preconditioner and the Generalized Superoptimal Preconditioner
Hong-Kui Pang 1*, Xiao-Qing Jin 11 Department of Mathematics, University of Macau, Macao, China.
Received 6 August 2009; Accepted (in revised version) 31 August 2009
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  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.AMS subject classifications: 65F10, 65F15, 65F35, 65F99
Key words: Optimal preconditioner, generalized superoptimal preconditioner, Moore-Penrose inverse, unitarily invariant norm, semi-stability, singular value.
Email: email@example.com (H.-K. Pang), firstname.lastname@example.org (X.-Q. Jin)