The study of new fixed-point iteration schemes for solving absolute value equations.
Rashid Ali1, Zhao Zhang1, Fuad A Awwad2
1School of Mathematical Sciences, Zhejiang Normal University, Jinhua 321004, Zhejiang, PR China.
Heliyon
|August 16, 2024
Summary
New fixed-point iteration schemes effectively solve absolute value equations (AVEs), demonstrating convergence and advantages in scientific computing and operations research.
Area of Science:
- Numerical analysis
- Applied mathematics
- Scientific computing
Background:
- Absolute value equations (AVEs) are fundamental in diverse scientific and engineering fields.
- Existing methods for solving AVEs may have limitations in certain complex scenarios.
Purpose of the Study:
- To introduce novel fixed-point iteration schemes for solving absolute value equations.
- To establish convergence criteria for the proposed methods under specific conditions.
Main Methods:
- Development of two distinct fixed-point iteration algorithms.
- Theoretical analysis to determine convergence properties.
- Numerical experimentation to validate performance.
Main Results:
- The proposed schemes demonstrate effective solutions for AVEs.
- Convergence is proven under defined theoretical conditions.
- Numerical examples highlight the superior performance of the new methods.
Conclusions:
- The presented fixed-point iteration schemes offer a promising advancement for solving AVEs.
- The findings encourage further research into advanced numerical techniques for complex equations.
Keywords:
49M2090C3390C59Absolute value equationsConvergence theoryFixed-point schemesNumerical resultsMore Related Videos
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