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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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Approximation properties of multivariate wavelets
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by Rong-Qing Jia PDF
Math. Comp. 67 (1998), 647-665 Request permission


Wavelets are generated from refinable functions by using multiresolution analysis. In this paper we investigate the approximation properties of multivariate refinable functions. We give a characterization for the approximation order provided by a refinable function in terms of the order of the sum rules satisfied by the refinement mask. We connect the approximation properties of a refinable function with the spectral properties of the corresponding subdivision and transition operators. Finally, we demonstrate that a refinable function in $W_{1}^{k-1}(\mathbb {R}^{s})$ provides approximation order $k$.
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Additional Information
  • Rong-Qing Jia
  • Affiliation: Department of Mathematical Sciences, University of Alberta, Edmonton, Alberta, Canada T6G 2G1
  • Email:
  • Received by editor(s): April 17, 1996
  • Additional Notes: Supported in part by NSERC Canada under Grant OGP 121336.
  • © Copyright 1998 American Mathematical Society
  • Journal: Math. Comp. 67 (1998), 647-665
  • MSC (1991): Primary 41A25, 41A63; Secondary 42C15, 65D15
  • DOI:
  • MathSciNet review: 1451324