Khani, M.H., Rashidinia, J. and Zia Borujeni, S. (2015) Application of Different H(x) in Homotopy Analysis Methods for Solving Systems of Linear Equations. Advances in Linear Algebra & Matrix Theory, 5, 129-137. - References

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Khani, M.H., Rashidinia, J. and Zia Borujeni, S. (2015) Application of Different H(x) in Homotopy Analysis Methods for Solving Systems of Linear Equations. Advances in Linear Algebra & Matrix Theory, 5, 129-137.
http://dx.doi.org/10.4236/alamt.2015.53012

has been cited by the following article:

TITLE: A New Approximation to the Linear Matrix Equation AX = B by Modification of He’s Homotopy Perturbation Method

AUTHORS: Amir Sadeghi

KEYWORDS: Matrix Equation, Homotopy Perturbation Method, Convergence, Diagonally Dominant Matrix, Regular Splitting

JOURNAL NAME: Advances in Linear Algebra & Matrix Theory, Vol.6 No.2, May 26, 2016

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.