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Fitting a Cm-smooth function to data, III
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DOI：10.4007/annals.2009.170.427.png)
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Abstract
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Fix m, n >= 1. Given an N-point set E subset of R-n, we exhibit a list of O(N) subsets S-1, S-2,..., S-L subset of E, each containing O(1) points, such that the following holds: Let f : E -> R-n. Suppose that, for each l = 1,..., L, there exists F-l is an element of C-m (R-n) with norm <= 1, agreeing with f on S-l. Then there exists F is an element of C-m (R-n), with norm O (1), agreeing with f on E. We give an application to the problem of discarding outliers from the set E.
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