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Robust solutions to least-squares problems with uncertain data. (English) Zbl 0891.65039

Least-squares problems are studied where the coefficient matrices are unknown but bounded. The worse-case residual error is minimized. The exact value of the optimal worst-case residuals is computed using convex, second-order cone programming or semidefinite programming. A consequence is that the minimizing vector can be computed in polynomial time.

MSC:

65F20 Numerical solutions to overdetermined systems, pseudoinverses
65Y20 Complexity and performance of numerical algorithms
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