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Smoothing and interpolation in a convex subset of a Hilbert space. (English) Zbl 0651.65046

Some basic facts on best interpolation and smoothing subject to convex constraints in Hilbert space are presented. The problem of finding the least norm solution satisfying the constraints is split into, first, finding the orthogonal projection onto the constraint set and, second, fitting the interpolation or smoothing conditions by solving a finite dimensional dual extremal problem. The results are given, first, when the constraints set is a convex cone, and then in the general case. Concrete examples and applications of the author’s approach are given: convex optimal spline interpolation, positive thin plate splines, numerical solution of one problem in EXAFS spectroscopy.
Reviewer: V.V.Kobkov

MSC:

65J05 General theory of numerical analysis in abstract spaces
41A65 Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)
65D10 Numerical smoothing, curve fitting
65D07 Numerical computation using splines
41A15 Spline approximation
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