TY - JOUR
T1 - Some Properties of the Optimal Preconditioner and the Generalized Superoptimal Preconditioner
AU - Hong-Kui Pang & Xiao-Qing Jin
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 - <p style="text-align: justify;">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.</p>