Minimal properties of the Drazin-inverse solution of a matrix equation

被引：0

作者：

Miladinovic, Marko ^{[1
]}

Miljkovic, Sladjana ^{[1
]}

Stanimirovic, Predrag S. ^{[1
]}

机构：

[1] Univ Nis, Fac Sci & Math, Nish, Serbia

来源：

FILOMAT | 2014年 / 28卷 / 02期

关键词：

Drazin inverse; Drazin-inverse solution; generalized inverses; least-squares solutions; matrix equation; CRAMER RULE; SYSTEMS; INDEX;

D O I：

10.2298/FIL1402383M

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We present the Drazin-inverse solution of the matrix equation AXB = G as a least-squares solution of a specified minimization problem. Some important properties of the Moore-Penrose inverse are extended on the Drazin inverse by exploring the minimal norm properties of the Drazin-inverse solution of the matrix equation AXB = G. The least squares properties of the Drazin-inverse solution lead to new representations of the Drazin inverse of a given matrix, which are justified by illustrative examples.

引用

页码：383 / 395

页数：13

共 50 条

[1] Gradient methods for computing the Drazin-inverse solution
Miljkovic, Sladjana
Miladinovic, Marko
Stanimirovic, Predrag S.
Wei, Yimin
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2013, 253 : 255 - 263
[2] Condition number for the Drazin inverse and the Drazin-inverse solution of singular linear system with their condition numbers
Wei, YM
Diao, H
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2005, 182 (02) : 270 - 289
[3] Minimization of quadratic forms using the Drazin-inverse solution
Stanimirovic, Predrag S.
Pappas, Dimitrios
Miljkovic, Sladjana
LINEAR & MULTILINEAR ALGEBRA, 2014, 62 (02): : 252 - 266
[4] New methods for computing the Drazin-inverse solution of singular linear systems
Toutounian, F.
Buzhabadi, R.
APPLIED MATHEMATICS AND COMPUTATION, 2017, 294 : 343 - 352
[5] DGMRES method augmented with eigenvectors for computing the Drazin-inverse solution of singular linear systems
Bin Meng
Acta Mathematicae Applicatae Sinica, English Series, 2016, 32 : 549 - 558
[6] DGMRES Method Augmented with Eigenvectors for Computing the Drazin-inverse Solution of Singular Linear Systems
Bin MENG
Acta Mathematicae Applicatae Sinica, 2016, 32 (02) : 549 - 558
[7] DGMRES Method Augmented with Eigenvectors for Computing the Drazin-inverse Solution of Singular Linear Systems
Meng, Bin
ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES, 2016, 32 (02): : 549 - 558
[8] Orthogonal polynomials and semi-iterative methods for the Drazin-inverse solution of singular linear systems
Avram Sidi
Yuliya Kanevsky
Numerische Mathematik, 2003, 93 : 563 - 581
[9] A unified approach to Krylov subspace methods for the Drazin-inverse solution of singular nonsymmetric linear systems
Sidi, A
LINEAR ALGEBRA AND ITS APPLICATIONS, 1999, 298 (1-3) : 99 - 113
[10] DGMRES: A GMRES-type algorithm for Drazin-inverse solution of singular nonsymmetric linear systems
Sidi, A
LINEAR ALGEBRA AND ITS APPLICATIONS, 2001, 335 : 189 - 204

← 1 2 3 4 5 →