Some Iterative Methods Of The Drazin Inverse

In this note,we construct new iterative methods for computing the Drazin inverse. The paper is organized as follows:In chapter 1,we give some required preparative knowledge including general sym-bols,definitions and basic lemmas.Also,we present the main results of the note.In chapter 2,we construct a new iterative method for computing the Drazin inverse and deduce the necessary and sufficient condition for its convergence to Ad.Moreover, we present the error bounnds.In chapter 3,we present the iterative methods for computing the generalized inverse AT,S(2) over Banach spaces,and also for computing the generalized Drazin inverses of Ba-nach algebra elements.We also reveal the intrinsic relationship between the convergence of such iterations and the existence of AT,S(2).Moreover,the necessary and sufficient con-ditions for iterative convergence and present the error bounds of the iterative methods.In chapter 4,we give four iterative formulas by using theα-βgeneralized inverse and its correlational properties.Also,we prove the necessary and sufficient conditions for iterative convergence and estimate the error bounds.