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.
Ameri, A., & Panjeh Ali Beik, F. (2021). Note to the convergence of minimum residual HSS method. Journal of Mathematical Modeling, 9(2), 323-330. doi: 10.22124/jmm.2020.18109.1559
MLA
Arezo Ameri; Fatemeh Panjeh Ali Beik. "Note to the convergence of minimum residual HSS method". Journal of Mathematical Modeling, 9, 2, 2021, 323-330. doi: 10.22124/jmm.2020.18109.1559
HARVARD
Ameri, A., Panjeh Ali Beik, F. (2021). 'Note to the convergence of minimum residual HSS method', Journal of Mathematical Modeling, 9(2), pp. 323-330. doi: 10.22124/jmm.2020.18109.1559
VANCOUVER
Ameri, A., Panjeh Ali Beik, F. Note to the convergence of minimum residual HSS method. Journal of Mathematical Modeling, 2021; 9(2): 323-330. doi: 10.22124/jmm.2020.18109.1559
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