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Volume 40, Issue 3
The AOR-Base Splitting Modified Fixed Point Iteration for Solving Absolute Value Equations

Changfeng Ma & Jing Kang

DOI: 10.4208/cmr.2024-0009

Commun. Math. Res., 40 (2024), pp. 261-274.

Published online: 2024-09

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  • Abstract

Recently, Yu et al. presented a modified fixed point iterative (MFPI) method for solving large sparse absolute value equation (AVE). In this paper, we consider using accelerated overrelaxation (AOR) splitting to develop the modified fixed point iteration (denoted by MFPI-JS and MFPI-GSS) methods for solving AVE. Furthermore, the convergence analysis of the MFPI-JS and MFPI-GSS methods for AVE are also studied under suitable restrictions on the iteration parameters, and the functional equation between the parameter $\tau$ and matrix $Q.$ Finally, numerical examples show that the MFPI-JS and MFPI-GSS are efficient iteration methods.

  • Keywords

Absolute value equation, modified point iteration, convergence analysis, numerical experiment.

  • AMS Subject Headings

65H10, 65F10

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CMR-40-261, author = {Ma , Changfeng and Kang , Jing}, title = {The AOR-Base Splitting Modified Fixed Point Iteration for Solving Absolute Value Equations}, journal = {Communications in Mathematical Research }, year = {2024}, volume = {40}, number = {3}, pages = {261--274}, abstract = {

Recently, Yu et al. presented a modified fixed point iterative (MFPI) method for solving large sparse absolute value equation (AVE). In this paper, we consider using accelerated overrelaxation (AOR) splitting to develop the modified fixed point iteration (denoted by MFPI-JS and MFPI-GSS) methods for solving AVE. Furthermore, the convergence analysis of the MFPI-JS and MFPI-GSS methods for AVE are also studied under suitable restrictions on the iteration parameters, and the functional equation between the parameter $\tau$ and matrix $Q.$ Finally, numerical examples show that the MFPI-JS and MFPI-GSS are efficient iteration methods.

}, issn = {2707-8523}, doi = {https://doi.org/10.4208/cmr.2024-0009}, url = {http://global-sci.org/intro/article_detail/cmr/23412.html} }
TY - JOUR T1 - The AOR-Base Splitting Modified Fixed Point Iteration for Solving Absolute Value Equations AU - Ma , Changfeng AU - Kang , Jing JO - Communications in Mathematical Research VL - 3 SP - 261 EP - 274 PY - 2024 DA - 2024/09 SN - 40 DO - http://doi.org/10.4208/cmr.2024-0009 UR - https://global-sci.org/intro/article_detail/cmr/23412.html KW - Absolute value equation, modified point iteration, convergence analysis, numerical experiment. AB -

Recently, Yu et al. presented a modified fixed point iterative (MFPI) method for solving large sparse absolute value equation (AVE). In this paper, we consider using accelerated overrelaxation (AOR) splitting to develop the modified fixed point iteration (denoted by MFPI-JS and MFPI-GSS) methods for solving AVE. Furthermore, the convergence analysis of the MFPI-JS and MFPI-GSS methods for AVE are also studied under suitable restrictions on the iteration parameters, and the functional equation between the parameter $\tau$ and matrix $Q.$ Finally, numerical examples show that the MFPI-JS and MFPI-GSS are efficient iteration methods.

Ma , Changfeng and Kang , Jing. (2024). The AOR-Base Splitting Modified Fixed Point Iteration for Solving Absolute Value Equations. Communications in Mathematical Research . 40 (3). 261-274. doi:10.4208/cmr.2024-0009
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