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Properties and Representations of Generalized Inverse on Algebraic Perturbation and Minimal Property of Condition Number on Drazin Inverse

Author: CaoLiQiong
Tutor: ChenGuoLiang
School: East China Normal University
Course: Computational Mathematics
Keywords: Algebraic Perturbation ( Weighted ) Drazin inverse ( Generalized ) Bott-Duffin inverse P- division ring Condition number Value range with zero space Matrix norm Non - negative matrix
CLC: O241.6
Type: Master's thesis
Year: 2005
Downloads: 103
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Abstract


Representation of the generalized inverse matrix calculation is an important research topic of the theory of generalized inverse , has been because of its the theoretically important position , and widely used in the actual concern for people , the past two to three decades , many scholars at home and abroad to do in this regard a lot of work to get the results ( see [ 1-6] ) . Different from the traditional analysis of disturbance , JRBunch and DJRose first proposed in 1974 , using algebraic perturbation method for solving non- singular linear equations subsequently , LBRall, Chen Yonglin , quarter, equalization of the use of the methods have been Banach space on linear operators , real (complex ) matrix domain { 1 } inverse , { 1,2} inverse and AT, S ( 2 ??) the inverse of a series of results . Weighted Drazin inverse of Chapter disturbances algebraic thinking , the first L- zero matrix (generalized ) Bott - Duffin inverse matrix and matrix number of new nature , and these two types of generalized inverse of the new expression . View of the addition to important applications in the fields of engineering , physics , Central Chapter will generalized inverse system P- addition to the ring has many nature be finishing . And P- addition to the ring for the first time to study the the matrix algebra perturbation theory . The condition number is a measure of the matrix , one of the main indicators of the degree of sensitivity disturbance plays an important role in the study of matrix calculations and perturbation analysis , to wide attention ( see [ 3,32-47 ] ) . Chapter 1 of this article will discuss the minimal nature of the condition number of Drazin inverse and Drazin inverse condition number to the minimum necessary and sufficient conditions , as well as the nature of the matrix has . Non - negative matrix has a wide range of applications in stochastic processes , Markov chains , mathematical statistics . Chapter 1 of this article will discuss a special class of non- negative matrix . From a new point of departure , the number of new properties in the further discussion .

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CLC: > Mathematical sciences and chemical > Mathematics > Computational Mathematics > Numerical Analysis > Linear algebra method of calculating
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