A new method for solving ill-conditioned linear systems

Abstract

An accurate numerical method is established for matrix inversion. It is shown theoretically that the scheme possesses the high order of convergence of seven. Subsequently, the method is taken into account for solving linear systems of equations. The accuracy of the contributed iterative method is clarified on solving numerical examples when the coefficient matrices are ill-conditioned. All of the computations are performed on a PC using several programs written in Mathematica 7.

Keywords

• matrix inversion
• linear systems
• Hilbert matrix
• ill-conditioned
• approximate inverse