Optimal backward perturbation bounds for the linear least squares problem
نویسندگان
چکیده
Dedicated to William Kahan and Beresford Parlett on the occasion of their 60th birthdays Let A be an m n matrix, b be an m-vector, and x̃ be a purported solution to the problem of minimizing kb Axk2. We consider the following open problem: find the smallest perturbation E of A such that the vector x̃ exactly minimizes kb (A+E)xk2. This problem is completely solved whenE 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.
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عنوان ژورنال:
- Numerical Lin. Alg. with Applic.
دوره 2 شماره
صفحات -
تاریخ انتشار 1995