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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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Polynomial approximation of functions in Sobolev spaces
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by Todd Dupont and Ridgway Scott PDF
Math. Comp. 34 (1980), 441-463 Request permission


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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Additional Information
  • © Copyright 1980 American Mathematical Society
  • Journal: Math. Comp. 34 (1980), 441-463
  • MSC: Primary 65D15; Secondary 41A10
  • DOI:
  • MathSciNet review: 559195