A Stable Iteration to the Matrix Inversion

The matrix inversion plays a signicant role in engineering and sciences. Any nonsingular square matrix has a unique inverse which can readily be evaluated via numeri- cal techniques such as direct methods, decomposition scheme, iterative methods, etc. In this research article, rst of all an algorithm which has fourth order rate of convergency with con- ditional 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. Fur- thermore, the convergence and stability properties of the proposed schemes will be analyzed in details. Numerical experiments are adopted to illustrate the properties of the modied methods.