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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.98.

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The $L_{2}$-approximation order of surface spline interpolation
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by Michael J. Johnson PDF
Math. Comp. 70 (2001), 719-737 Request permission

Abstract:

We show that if the open, bounded domain $\Omega \subset \mathbb {R}^{d}$ has a sufficiently smooth boundary and if the data function $f$ is sufficiently smooth, then the $L_{p}(\Omega )$-norm of the error between $f$ and its surface spline interpolant is $O(\delta ^{\gamma _{p}+1/2})$ ($1\leq p\leq \infty$), where $\gamma _{p}:=\min \{m,m-d/2+d/p\}$ and $m$ is an integer parameter specifying the surface spline. In case $p=2$, this lower bound on the approximation order agrees with a previously obtained upper bound, and so we conclude that the $L_{2}$-approximation order of surface spline interpolation is $m+1/2$.
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Additional Information
  • Michael J. Johnson
  • Affiliation: Deptartment of Mathematics and Computer Science, Kuwait University, P.O. Box 5969, 13060 Safat, Kuwait
  • Email: johnson@mcc.sci.kuniv.edu.kw
  • Received by editor(s): June 10, 1999
  • Published electronically: October 27, 2000
  • Additional Notes: This work was supported by Kuwait University Research Grant SM-175.
  • © Copyright 2000 American Mathematical Society
  • Journal: Math. Comp. 70 (2001), 719-737
  • MSC (2000): Primary 41A15, 41A25, 41A63, 65D05
  • DOI: https://doi.org/10.1090/S0025-5718-00-01301-6
  • MathSciNet review: 1813145