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An inversion-free method for finding positive definite solution of a rational matrix equation.
Fazlollah Soleymani1, Mahdi Sharifi1, Solat Karimi Vanani1
1Department of Mathematics, Islamic Azad University, Shahrekord Branch, Shahrekord, Iran.
Thescientificworldjournal
|September 13, 2014
Summary
A novel iterative method finds the minimal solution for a rational matrix equation without matrix inversion. This inversion-free approach demonstrates convergence through numerical experiments.
Area of Science:
- Numerical analysis
- Matrix theory
- Computational mathematics
Background:
- Rational matrix equations are fundamental in various scientific and engineering disciplines.
- Solving these equations often involves computationally intensive methods, such as matrix inversion.
Purpose of the Study:
- To develop a new iterative scheme for solving rational matrix equations.
- To provide an inversion-free computational method for finding the minimal solution.
Main Methods:
- Construction of a new iterative scheme.
- Analysis of the scheme's convergence properties.
- Validation through numerical experiments.
Main Results:
- An inversion-free iterative method for solving X + A*X^(-1)A = I was successfully developed.
- The convergence of the proposed iterative scheme was theoretically studied.
- Numerical experiments confirmed the practical performance and convergence of the method.
Conclusions:
- The new iterative scheme offers an efficient alternative for solving this class of rational matrix equations.
- The inversion-free nature of the method reduces computational complexity.
- The study validates the method's applicability and reliability.
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