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Optimal backward perturbation bounds for the linear least squares problem (1995)

Waldén, Bertil ; Karlson, Rune ; Sun, Ji-Guang

New York, NY [u.a.] : Wiley-Blackwell

Numerical Linear Algebra with Applications 2 (1995), S. 271-286

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ISSN: 1070-5325

Keywords: linear least squares ; backward perturbations ; Engineering ; Engineering General

Source: Wiley InterScience Backfile Collection 1832-2000

Topics: Mathematics

Notes: Let A be an m × n matrix, b be an m-vector, and x̃ be a purported solution to the problem of minimizing ‖b - Ax‖2. We consider the following open problem: find the smallest perturbation E of A such that the vector x̃ exactly minimizes ‖b - (A+E)x‖2. This problem is completely solved when E is measured in the Frobenius norm. When using the spectral norm of E, upper and lower bounds are given, and the optimum is found under certain conditions.

Additional Material: 1 Tab.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1002/nla.1680020308

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