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Generalized and novel iterative scheme for best approximate solution of large and sparse augmented linear systems
Abdullah Mohammed Alomair1, Farooq Ahmed Shah2, Khaleel Ahmed2
1Department of Quantitative Methods, School of Business, King Faisal University, Al-Ahsa 31982, Saudi Arabia.
Heliyon
|August 22, 2024
Summary
A novel iterative technique offers rapid, approximate solutions for systems of linear equations. This method
Area of Science:
- Numerical Analysis
- Computational Mathematics
Background:
- Solving large systems of linear equations is crucial in science and engineering.
- Existing iterative methods like SOR-like and generalized SOR have limitations.
Purpose of the Study:
- Introduce a generalized novel iterative technique for linear systems.
- Analyze the performance and convergence of the new method.
Main Methods:
- Developed a new iterative scheme with adjustable parameters.
- Applied the technique to significant problems.
- Compared its effectiveness against modified SOR-like, generalized SOR, and SOR-like methods.
Main Results:
- The novel iterative technique demonstrates rapid and accurate approximate solutions.
- Theoretical convergence criteria are supported by numerical and graphical evidence.
- Outperforms existing methods in solving large systems of linear equations.
Conclusions:
- The generalized iterative technique is effective for solving systems of linear equations.
- Its detailed analysis and convergence criteria offer a valuable tool.
- Potential applications span various scientific and engineering disciplines.
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