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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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A posteriori improvements for interpolating periodic splines
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by Thomas R. Lucas PDF
Math. Comp. 40 (1983), 243-251 Request permission


A method of a posteriori improvements of interpolating periodic splines of order 2r and their derivatives over a uniform mesh is developed using polynomial-type correction terms. These improvements enhance the order of convergence by several powers of the step size h and are convenient and inexpensive to implement. The polynomials are specified in closed form using the Bernoulli numbers. That the first of these is related to the Bernoulli polynomial of degree 2r is due to Swartz [10], but no general development beyond the first has previously been made. These polynomials are multiplied by high order derivatives of the function evaluated at the mesh points. Some recent results by Lucas [8] are used to accurately estimate these values. Some numerical results are given which correspond closely with the predictions of the theory.
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Additional Information
  • © Copyright 1983 American Mathematical Society
  • Journal: Math. Comp. 40 (1983), 243-251
  • MSC: Primary 41A15; Secondary 65D07
  • DOI:
  • MathSciNet review: 679443