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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.

advances in linear algebra and matrix theory

A New Approximation to the Linear Matrix Equation &amp;lt;i&amp;gt;AX&amp;lt;/i&amp;gt; = &amp;lt;i&amp;gt;B&amp;lt;/i&amp;gt; by Modification of He’s Homotopy Perturbation Method