-
المقاله
1 - A new Approximation to the solution of the linear matrix equation AXB = CJournal of Linear and Topological Algebra , العدد 5 , السنة 4 , پاییز 2015It is well-known that the matrix equations play a significant role in several applications in science and engineering. There are various approaches either direct methods or iterative methods to evaluate the solution of these equations. In this research article, the homo أکثرIt is well-known that the matrix equations play a significant role in several applications in science and engineering. There are various approaches either direct methods or iterative methods to evaluate the solution of these equations. In this research article, the homotopy perturbation method (HPM) will employ to deduce the approximated solution of the linear matrix equation in the form AXB=C. Furthermore, the conditions will be explored to check the convergence of the homotopy series. Numerical examples are also adapted to illustrate the properties of the modified method. تفاصيل المقالة -
المقاله
2 - A stable iteration to the matrix inversionInternational Journal of Mathematical Modeling & Computations , العدد 5 , السنة 8 , پاییز 2018The matrix inversion plays a signifcant role in engineering and sciences. Any nonsingular square matrix has a unique inverse which can readily be evaluated via numerical techniques such as direct methods, decomposition scheme, iterative methods, etc. In this research ar أکثرThe matrix inversion plays a signifcant role in engineering and sciences. Any nonsingular square matrix has a unique inverse which can readily be evaluated via numerical techniques such as direct methods, decomposition scheme, iterative methods, etc. In this research article, first of all an algorithm which has fourth order rate of convergency with conditional stability will be proposed. Then, for solving stability issue, we introduce a coupled stable scheme that can evaluate the matrix inversion with very acceptable accuracy. Furthermore, the convergence and stability properties of the proposed schemes will be analyzed in details. Numerical experiments are adopted to illustrate the properties of the modified methods. تفاصيل المقالة