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Volume 15, Issue 3
Two-Step Two-Sweep Modulus-Based Matrix Splitting Iteration Method for Linear Complementarity Problems

Maryam Bashirizadeh & Masoud Hajarian

DOI: 10.4208/nmtma.OA-2021-0131

Numer. Math. Theor. Meth. Appl., 15 (2022), pp. 592-619.

Published online: 2022-07

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  • Abstract

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.

  • Keywords

Linear complementarity problem, modulus-based method, two-step, two sweep, $H_+$-matrix, convergence.

  • AMS Subject Headings

65F10, 65F15

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-15-592, author = {Bashirizadeh , Maryam and Hajarian , Masoud}, title = {Two-Step Two-Sweep Modulus-Based Matrix Splitting Iteration Method for Linear Complementarity Problems}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2022}, volume = {15}, number = {3}, pages = {592--619}, abstract = {

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} }
TY - JOUR T1 - Two-Step Two-Sweep Modulus-Based Matrix Splitting Iteration Method for Linear Complementarity Problems AU - Bashirizadeh , Maryam AU - Hajarian , Masoud JO - Numerical Mathematics: Theory, Methods and Applications VL - 3 SP - 592 EP - 619 PY - 2022 DA - 2022/07 SN - 15 DO - http://doi.org/10.4208/nmtma.OA-2021-0131 UR - https://global-sci.org/intro/article_detail/nmtma/20808.html KW - Linear complementarity problem, modulus-based method, two-step, two sweep, $H_+$-matrix, convergence. AB -

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.

Bashirizadeh , Maryam and Hajarian , Masoud. (2022). Two-Step Two-Sweep Modulus-Based Matrix Splitting Iteration Method for Linear Complementarity Problems. Numerical Mathematics: Theory, Methods and Applications. 15 (3). 592-619. doi:10.4208/nmtma.OA-2021-0131
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