scholarly journals Condition number for the Drazin inverse and the Drazin-inverse solution of singular linear system with their condition numbers

2005 ◽  
Vol 182 (2) ◽  
pp. 270-289 ◽  
Author(s):  
Yimin Wei ◽  
Huaian Diao
Keyword(s):  
Linear System ◽  
Condition Number ◽  
Inverse Solution ◽  
Drazin Inverse ◽  
Condition Numbers ◽  
Singular Linear System

scholarly journals Minimum property of condition numbers for the Drazin inverse and singular linear equations

Filomat ◽  
2018 ◽  
Vol 32 (7) ◽  
pp. 2685-2691
Author(s):  
Haifeng Ma
Keyword(s):  
Linear Equation ◽  
Small Perturbation ◽  
Linear Equations ◽  
Inverse Solution ◽  
Drazin Inverse ◽  
Condition Numbers ◽  
Perturbation Matrix

For a singular linear equation Ax = b,x ? R(AD), a small perturbation matrix E and a vector ?b are given to A and b, respectively. We then have the perturbed singular linear equation (A+E)~x = b+?b, ~x ? R[(A+E)D]. This note is devoted to show the minimum property of the condition numbers on the Drazin inverse AD and the Drazin-inverse solution ADb.

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