A modified fixed point iteration method for solving the system of absolute value equations

The fixed point iteration (FPI) method proposed by Ke [Appl Math Lett. 2020;99:105990] for solving the absolute value equations (AVE) with the form is interesting for its simplicity and efficiency. However, its convergence is only guaranteed for the case that , excluding the possible case that . To...

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Bibliographic Details
Published inOptimization Vol. 71; no. 3; pp. 449 - 461
Main Authors Yu, Dongmei, Chen, Cairong, Han, Deren
Format Journal Article
LanguageEnglish
Published Philadelphia Taylor & Francis 04.03.2022
Taylor & Francis LLC
Subjects
Absolute value equations
Convergence
fixed point iteration
Iterative methods
linear convergence
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Summary:The fixed point iteration (FPI) method proposed by Ke [Appl Math Lett. 2020;99:105990] for solving the absolute value equations (AVE) with the form is interesting for its simplicity and efficiency. However, its convergence is only guaranteed for the case that , excluding the possible case that . To complete the gap, we develop a modified FPI (MFPI) method for solving the AVE with , which, besides keeping the simplicity of FPI, improves its efficiency by judiciously choosing the involving parameter. Under mild conditions, we prove its linear convergence. We present some preliminary numerical results for , demonstrating its convergence; and compare it with FPI when , illustrating its superiority.
ISSN:0233-1934
1029-4945
DOI:10.1080/02331934.2020.1804568