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

Abstract:

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: jia@xihu.math.ualberta.ca
  • 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: https://doi.org/10.1090/S0025-5718-98-00925-9
  • MathSciNet review: 1451324