GENERALIZED SOR-LIKE ITERATION METHODS FOR ABSOLUTE VALUE EQUATIONS ASSOCIATED WITH CIRCULAR CONES

Weihua Lin

doi:10.11948/20250378

2026 Volume 16 Issue 5

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Article navigation > Journal of Applied Analysis & Computation > 2026 > 16(5): 2497-2514

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Weihua Lin. GENERALIZED SOR-LIKE ITERATION METHODS FOR ABSOLUTE VALUE EQUATIONS ASSOCIATED WITH CIRCULAR CONES[J]. Journal of Applied Analysis & Computation, 2026, 16(5): 2497-2514. doi: 10.11948/20250378

Citation:

Weihua Lin. GENERALIZED SOR-LIKE ITERATION METHODS FOR ABSOLUTE VALUE EQUATIONS ASSOCIATED WITH CIRCULAR CONES[J]. Journal of Applied Analysis & Computation, 2026, 16(5): 2497-2514. doi: 10.11948/20250378

GENERALIZED SOR-LIKE ITERATION METHODS FOR ABSOLUTE VALUE EQUATIONS ASSOCIATED WITH CIRCULAR CONES

Weihua Lin^1, ,

1.
School of Mathematics and Statistics, Hanshan Normal University, Chaozhou 521041, Guangdong, China

Corresponding author: Email: 740816193@qq.com(W. Lin)
Fund Project: This research is supported by Ministry of Education Humanities and Social Sciences Research Planning Fund Project (Theoretical Deduction and Mechanism Design for High-Quality Development of China's Professional Football League, 24YJA890014); Guangdong Provincial Higher Education Teaching Research and Reform Project (Research and Practice on Teaching Reform of Mathematics Teaching Method Course under Core Literacy); Research Project of Hanshan Normal University (Application of Grey Rough Set Method in Quantitative Research on Mathematical Emotional Literacy with Missing Data, XGPY202403); 2025 Hanshan Normal University Smart Course Construction Project Approval (Mathematics Subject Teaching Methodology, Yue Han Shi [2025] No. 223); Hanshan Normal University Expert Studio for Primary and Secondary School Teacher Training (Yue Han Shi [2026] No. 31)

Abstract

Abstract

In this paper, we study the absolute value equations associated with circular cones (referred to as CCAVE). The circular cone is a type of non-symmetric cone that generalizes the second-order cone. By equivalently reformulating CCAVE as a two-by-two block nonlinear equation, we propose a class of generalized SOR-like iteration methods for solving CCAVE. Useful properties of the circular cone are explored, and sufficient conditions for ensuring the convergence of the generalized SOR-like iteration methods are analyzed. Numerical experiments demonstrate the effectiveness of the proposed methods in solving CCAVE.
- Circular cone /
- absolute value equation /
- matrix splitting /
- convergence
MSC: 65F10, 65H10

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References

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