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Note to the convergence of minimum residual HSS method | ||
| Journal of Mathematical Modeling | ||
| دوره 9، شماره 2، مرداد 2021، صفحه 323-330 اصل مقاله (296.01 K) | ||
| نوع مقاله: Research Article | ||
| شناسه دیجیتال (DOI): 10.22124/jmm.2020.18109.1559 | ||
| نویسندگان | ||
| Arezo Ameri1؛ Fatemeh Panjeh Ali Beik* 2 | ||
| 1Department of Mathematics, Kerman Branch, Islamic Azad University, Kerman, Iran | ||
| 2Department of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran | ||
| چکیده | ||
| 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. | ||
| کلیدواژه‌ها | ||
| Minimum residual technique؛ Hermitian and skew-Hermitian splitting؛ two-step iterative method؛ Convergence | ||
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