Numer. Math. Theor. Meth. Appl., 15 (2022), pp. 592-619.
Published online: 2022-07
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Linear complementarity problems have drawn considerable attention in recent years due to their wide applications. In this article, we introduce the two-step two-sweep modulus-based matrix splitting (TSTM) iteration method and two-sweep modulus-based matrix splitting type II (TM II) iteration method which are a combination of the two-step modulus-based method and the two-sweep modulus-based method, as two more effective ways to solve the linear complementarity problems. The convergence behavior of these methods is discussed when the system matrix is either a positive-definite or an $H_+$-matrix. Finally, numerical experiments are given to show the efficiency of our proposed methods.
}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2021-0131}, url = {http://global-sci.org/intro/article_detail/nmtma/20808.html} }Linear complementarity problems have drawn considerable attention in recent years due to their wide applications. In this article, we introduce the two-step two-sweep modulus-based matrix splitting (TSTM) iteration method and two-sweep modulus-based matrix splitting type II (TM II) iteration method which are a combination of the two-step modulus-based method and the two-sweep modulus-based method, as two more effective ways to solve the linear complementarity problems. The convergence behavior of these methods is discussed when the system matrix is either a positive-definite or an $H_+$-matrix. Finally, numerical experiments are given to show the efficiency of our proposed methods.