A Numerical Method for Accelerating the Convergence of the Power Method

Abstract

ABSTRACT This paper describes a procedure which combines between the Wilkinson and Aitken methods in order to obtain a best approximation of the greatest eigenvalue. Both the symmetric and the nonsymmetric matrices are solved. It shows that our suggested method converges quickly and it is quit insensitive to the properties of the matrices used. A comparison between these approximations for five numerical examples is given, depending on the number of iterations and running computer time. Experimental results indicate that the new numerical procedure is more efficient than Power, Wilkinson and Aitken methods.

Keywords

• numerical method
• accelerate the convergence
• the power method