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The Inversion of Multiscale Convolution Approximation and Average of Distributions

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Abstract

We develop two kinds of inversion formulas of the multiscale convolution approximation which is defined by a convolution kernel φ. The inversion formulas are constructed by a convolution kernel ψ which is defined in terms of φ and has a vanishing moment of order one. A large class of generalized moving average approximations with B-splines, Box-splines and exponential Box-splines (EB-splines) as convolution kernels φ is included in the theory formulated in this paper. The average of distributions is considered, and correspondingly, the formulas related to the EB-splines are obtained from the δ-average.

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Authors and Affiliations

  1. Department of Scientific Computation and Computer Applications, Zhongshan University, Guangzhou, 510275, China

    Yuesheng Li

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  1. Yuesheng Li
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Li, Y. The Inversion of Multiscale Convolution Approximation and Average of Distributions. Advances in Computational Mathematics 19, 293–306 (2003). https://doi.org/10.1023/A:1022811005225

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  • DOI: https://doi.org/10.1023/A:1022811005225

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