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A New Approximation to the Linear Matrix Equation <i>AX</i> = <i>B</i> by Modification of He’s Homotopy Perturbation Method
Young Researchers and Elite Club, Robat Karim Branch, Islamic Azad University, Tehran, Iran
- 1 Young Researchers and Elite Club, Robat Karim Branch, Islamic Azad University, Tehran, Iran
Advances in Linear Algebra & Matrix Theory·Volume 06 (2016)·Pages 23–30·Published 26 May 2016·DOI10.4236/alamt.2016.62004
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Abstract
It is well known that the matrix equations play a significant role in engineering and applicable sciences. In this research article, a new modification of the homotopy perturbation method (HPM) will be proposed to obtain the approximated solution of the matrix equation in the form AX = B . Moreover, the conditions are deduced to check the convergence of the homotopy series. Numerical implementations are adapted to illustrate the properties of the modified method.
KeywordsMatrix EquationHomotopy Perturbation MethodConvergenceDiagonally Dominant MatrixRegular Splitting
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