A stable iteration to the matrix inversion

International Journal of Mathematical Modelling & Computations

مقاله 3، دوره 8، 4 (FALL) - شماره پیاپی 32، بهمن 2018، صفحه 227-238   

نوع مقاله: Full Length Article

نویسنده

Amir Sadeghi^*

Department of Mathematics, Robat Karim Branch, Islamic Azad University, Tehran, Iran.

چکیده

The 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.

کلیدواژه‌ها

Matrix inversion؛ Iterative methods؛ convergence؛ Stability؛ Coupled recursion