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Abstract: A common problem in applied mathematics is to find a function in a Hilbertspace with prescribed best approximations from a finite number of closed vectorsubspaces. In the present paper we study the question of the existence ofsolutions to such problems. A finite family of subspaces is said to satisfy the\emph{Inverse Best Approximation Property IBAP} if there exists a point thatadmits any selection of points from these subspaces as best approximations. Weprovide various characterizations of the IBAP in terms of the geometry of thesubspaces. Connections between the IBAP and the linear convergence rate of theperiodic projection algorithm for solving the underlying affine feasibilityproblem are also established. The results are applied to problems in harmonicanalysis, integral equations, signal theory, and wavelet frames.



Author: P. L. Combettes, N. N. Reyes

Source: https://arxiv.org/







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