Modified Picard-like Method for Solving Absolute Value Equations
We present a modified Picard-like method to solve absolute value equations by equivalently expressing the implicit fixed-point equation form of the absolute value equations as a two-by-two block nonlinear equation. This unifies some existing matrix splitting algorithms and improves the efficiency of...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-02-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/4/848 |
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| author | Yuan Liang Chaoqian Li |
| author_facet | Yuan Liang Chaoqian Li |
| author_sort | Yuan Liang |
| collection | DOAJ |
| description | We present a modified Picard-like method to solve absolute value equations by equivalently expressing the implicit fixed-point equation form of the absolute value equations as a two-by-two block nonlinear equation. This unifies some existing matrix splitting algorithms and improves the efficiency of the algorithm by introducing the parameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ω</mi></semantics></math></inline-formula>. For the choice of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ω</mi></semantics></math></inline-formula> in the new method, we give a way to determine the quasi-optimal values. Numerical examples are given to show the feasibility of the proposed method. It is also shown that the new method is better than those proposed by Ke and Ma in 2017 and Dehghan and Shirilord in 2020. |
| first_indexed | 2024-03-11T08:28:33Z |
| format | Article |
| id | doaj.art-a3522c069779466e8d52186e4a515670 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-11T08:28:33Z |
| publishDate | 2023-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-a3522c069779466e8d52186e4a5156702023-11-16T21:54:51ZengMDPI AGMathematics2227-73902023-02-0111484810.3390/math11040848Modified Picard-like Method for Solving Absolute Value EquationsYuan Liang0Chaoqian Li1School of Mathematics and Computer Science, Yunnan Minzu University, Kunming 650504, ChinaSchool of Mathematics and Statistics, Yunnan University, Kunming 650504, ChinaWe present a modified Picard-like method to solve absolute value equations by equivalently expressing the implicit fixed-point equation form of the absolute value equations as a two-by-two block nonlinear equation. This unifies some existing matrix splitting algorithms and improves the efficiency of the algorithm by introducing the parameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ω</mi></semantics></math></inline-formula>. For the choice of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ω</mi></semantics></math></inline-formula> in the new method, we give a way to determine the quasi-optimal values. Numerical examples are given to show the feasibility of the proposed method. It is also shown that the new method is better than those proposed by Ke and Ma in 2017 and Dehghan and Shirilord in 2020.https://www.mdpi.com/2227-7390/11/4/848splittingabsolute value equationPicard-like methoditeration |
| spellingShingle | Yuan Liang Chaoqian Li Modified Picard-like Method for Solving Absolute Value Equations Mathematics splitting absolute value equation Picard-like method iteration |
| title | Modified Picard-like Method for Solving Absolute Value Equations |
| title_full | Modified Picard-like Method for Solving Absolute Value Equations |
| title_fullStr | Modified Picard-like Method for Solving Absolute Value Equations |
| title_full_unstemmed | Modified Picard-like Method for Solving Absolute Value Equations |
| title_short | Modified Picard-like Method for Solving Absolute Value Equations |
| title_sort | modified picard like method for solving absolute value equations |
| topic | splitting absolute value equation Picard-like method iteration |
| url | https://www.mdpi.com/2227-7390/11/4/848 |
| work_keys_str_mv | AT yuanliang modifiedpicardlikemethodforsolvingabsolutevalueequations AT chaoqianli modifiedpicardlikemethodforsolvingabsolutevalueequations |