%0 Journal Article
%T Note to the convergence of minimum residual HSS method
%J Journal of Mathematical Modeling
%I University of Guilan
%Z 2345-394X
%A Ameri, Arezo
%A Panjeh Ali Beik, Fatemeh
%D 2021
%\ 05/01/2021
%V 9
%N 2
%P 323-330
%! Note to the convergence of minimum residual HSS method
%K Minimum residual technique
%K Hermitian and skew-Hermitian splitting
%K two-step iterative method
%K Convergence
%R 10.22124/jmm.2020.18109.1559
%X The minimum residual HSS (MRHSS) method is proposed in [BIT Numerical Mathematics, 59 (2019) 299--319] and its convergence analysis is proved under a certain condition. More recently in [Appl. Math. Lett. 94 (2019) 210--216], an alternative version of MRHSS is presented which converges unconditionally. In general, as the second approach works with a weighted inner product, it consumes more CPU time than MRHSS to converge. In the current work, we revisit the convergence analysis of the MRHSS method using a different strategy and state the convergence result for general two-step iterative schemes. It turns out that a special choice of parameters in the MRHSS results in an unconditionally convergent method without using a weighted inner product. Numerical experiments confirm the validity of established results.
%U https://jmm.guilan.ac.ir/article_4457_ff5133b3aab29d48f60bd3c444cb7bfd.pdf