On the computation of optimal approximations in Sard corner spaces
Franke, Richard H.
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The subject of linear optimal approximation has received considerable attention in recent years , , , , . The subject of multivariate approximation for scattered data, including optimal approximations, is reviewed in . The idea is appealing since the optimal approximation in a certain space of functions minimizes the norm of the error functional for approximations in that space. When the space is a Hilbert space, the computation of optimal approximations becomes rather simple, in theory . A known reproducing kernel function provides the representers of linear functional s defined on the space. The optimal approximation satisfies the system of equations obtained by requiring that the approximation be exact for the representers of the functional s being used for the approximation, usually point evaluation functionals.
NPS Report NumberNPS-53Fe76121
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