University of GuilanJournal of Mathematical Modeling2345-394X9220210501Note to the convergence of minimum residual HSS method323330445710.22124/jmm.2020.18109.1559ENArezoAmeriDepartment of Mathematics, Kerman Branch, Islamic Azad University, Kerman, IranFatemehPanjeh Ali BeikDepartment of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, IranJournal Article20201106The 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.https://jmm.guilan.ac.ir/article_4457_ff5133b3aab29d48f60bd3c444cb7bfd.pdf