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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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Sobolev-type approximation rates for divergence-free and curl-free RBF interpolants
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by Edward J. Fuselier PDF
Math. Comp. 77 (2008), 1407-1423 Request permission


Recently, error estimates have been made available for divergence-free radial basis function (RBF) interpolants. However, these results are only valid for functions within the associated reproducing kernel Hilbert space (RKHS) of the matrix-valued RBF. Functions within the associated RKHS, also known as the “native space” of the RBF, can be characterized as vector fields having a specific smoothness, making the native space quite small. In this paper we develop Sobolev-type error estimates when the target function is less smooth than functions in the native space.
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Additional Information
  • Edward J. Fuselier
  • Affiliation: Department of Mathematical Sciences, United States Military Academy, West Point, New York 10996
  • Email:
  • Received by editor(s): June 5, 2006
  • Received by editor(s) in revised form: April 8, 2007
  • Published electronically: December 27, 2007
  • Additional Notes: The results are part of the author’s dissertation written under the guidance of Francis Narcowich and Joe Ward at Texas A&M University, College Station, Texas 77843
  • Journal: Math. Comp. 77 (2008), 1407-1423
  • MSC (2000): Primary 41A63, 41A05; Secondary 41A30, 65D05
  • DOI:
  • MathSciNet review: 2398774