Iterative Methods To Compute The Generalized Inverse

The main aim of this paper is to compute the generalized inverse by constructing different kinds of iterative methods. The thesis is divided into three chapters:In chapter 1, we introduce the background, the present situation and the development trend of research on generalized inverse. We also introduce the necessary preliminaries such as the definitions, properties of range and the null-space on Banach spaces, spectrum radius, generalized inverse, semi-iterative method, higher-order iterative method, and the polar de-composition and so on.In chapter 2, the main aim of this chapter is to compute the generalized inverse AT,S(2) over Banach spaces by using semi-iterative method, and to present the error bounds of the semi-iterative method for approximating AT,S(2). And we also given the necessary and sufficient conditions for semi-iterative convergence to generalized inverse AT,S(2). The results of the paper are illustrated by numerical examples.In chapter 3, A higher-order iterative method for computing the polar decomposition of any arbitrary matrix is presented and analysed. It is shown analytically that the method is convergent and possesses seventh order. Acceleration parameters are introduced so as to enhance the initial rate of convergence.