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Optimal backward perturbation bounds for the linear least-squares problem with multiple right-hand sides
Umeå University, Faculty of Science and Technology, Departement of Computing Science.
1996 (English)In: Ima Journal of Numerical Analysis, Vol. 16, no 1, 1-11 p.Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
1996. Vol. 16, no 1, 1-11 p.
URN: urn:nbn:se:umu:diva-22001ISBN: 0272-4979OAI: diva2:212264
Available from: 2009-04-21 Created: 2009-04-21 Last updated: 2009-04-21

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