(untitled) (Journal of Computational Mathematics, 2007)
In this paper, we investigate the condition numbers for the generalized matrix inversion and the rank deficient linear least squares problem: _x \|Ax-b\|_2, where A is an m-by-n (m n) rank deficient matrix. We first derive an explicit expression for the condition number in the weighted Frobenius norm \|[AT, β b] \|_F of the data A and b, where T is a positive diagonal matrix and β is a positive scalar. We then discuss the sensitivity of the standard 2-norm condition numbers for the generalized matrix inversion and rank deficient least squares and establish relations between the condition numbers and their condition numbers called level-2 condition numbers.