Abstract
Let A be an m x n matrix, B be an m x r matrix, and (X) over tilde be an approximate solution to the problem of minimizing \\AX-B\\(F). In this note we consider the following open problem: find an explicit expression of the optimal backward perturbation bound eta(F)((X) over tilde) defined by eta(F)((X) over tilde)=min{\\(E,theta F)\\(F):(X) over tilde minimizes \\(A+E)X-(B+F)\\(F)} where theta is a positive number. This problem is solved when (X) over tilde is of full column rank.
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