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. and 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
Ameri, A. , and Panjeh Ali Beik, F. . "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
CHICAGO
A. Ameri and F. 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
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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