A New Proper-splitting Based On The Outer Inverse Of Matrices For Aingular Linear System

Splitting iterative method is commonly used methods for solving the linear equations Ax=b, in particular, parallel iteration method become an advanced research hotspot. When the coefficient matrix A is a singular or rectangular matrix, many scholars have studied the splitting method based on the M-P inverse in the literature [2,3,22], they have studied the convergence and rate of convergence of the matrix A, and gained rich conclusions. In this thesis, we introduce a conception of the splitting which is based on the general general-ized inverse (the outer inverse) of the matrix A, and researches the properties of the new types of the splitting.Firstly, in this thesis, based on V Agasthian’s work in [27] and Chen’s work in [30], we define new types of splittings based on a gen-eral generalized inverse AT,S(2) of the matrix A and present convergence results of different types of the splitting based on the outer inverse, namely, Weak Nonnegative Proper Splitting based on the out inverse, and Proper Regular Splitting based on the outer inverse. Secondly, we also present and derive some new comparison theorems between the spectral radii of matrix, these conclusions and concepts generalize and develop many existing results currently.The contributions of this thesis include:(1)We define new types of splittings based on the outer inverse of the matrix A and present the basic results of different types of the splitting based on the outer inverse.(2) We present convergence results of different types of the splitting based on the outer inverse and derive some new comparison theorems between the spectral radii of matrix...