@article { author = {Ameri, Arezo and Panjeh Ali Beik, Fatemeh}, title = {Note to the convergence of minimum residual HSS method}, journal = {Journal of Mathematical Modeling}, volume = {9}, number = {2}, pages = {323-330}, year = {2021}, publisher = {University of Guilan}, issn = {2345-394X}, eissn = {2382-9869}, doi = {10.22124/jmm.2020.18109.1559}, abstract = {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.}, keywords = {Minimum residual technique,Hermitian and skew-Hermitian splitting,two-step iterative method,Convergence}, url = {https://jmm.guilan.ac.ir/article_4457.html}, eprint = {https://jmm.guilan.ac.ir/article_4457_ff5133b3aab29d48f60bd3c444cb7bfd.pdf} }