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Polynomial approximation of functions in Sobolev spaces

Authors: Todd Dupont and Ridgway Scott
Journal: Math. Comp. 34 (1980), 441-463
MSC: Primary 65D15; Secondary 41A10
MathSciNet review: 559195
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Abstract: Constructive proofs and several generalizations of approximation results of J. H. Bramble and S. R. Hilbert are presented. Using an averaged Taylor series, we represent a function as a polynomial plus a remainder. The remainder can be manipulated in many ways to give different types of bounds. Approximation of functions in fractional order Sobolev spaces is treated as well as the usual integer order spaces and several nonstandard Sobolev-like spaces.

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Article copyright: © Copyright 1980 American Mathematical Society