ON THE PERTURBATION BOUND OF THE GROUP INVERSE WITH APPLICATION TO SINGULAR LINEAR SYSTEM
Yimin Wei · Chinese Annals of Mathematics,series A · 2003
A perturbation bound for the group inverse is developed. This bound is based on the Jordan canonical form and P-norm of A, where P is an invertible matrix such that and D is a nonsingular upper bidiagonal matrix withSharp estimates of p are derived when A and A + E are of the same rank and p is small. Under similar conditions the perturbation of a singular consistent linear system Ax = b is studied. Realistic bounds on the perturbation of xopi = A#b is presented, where xopt is the minimal P-norm solution.