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Generator, multiquadric generator, quasi-interpolation and multiquadric quasi-interpolation

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Abstract

The aim of this survey paper is to propose a new concept “generator”. In fact, generator is a single function that can generate the basis as well as the whole function space. It is a more fundamental concept than basis. Various properties of generator are also discussed. Moreover, a special generator named multiquadric function is introduced. Based on the multiquadric generator, the multiquadric quasi-interpolation scheme is constructed, and furthermore, the properties of this kind of quasi-interpolation are discussed to show its better capacity and stability in approximating the high order derivatives.

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Authors and Affiliations

  1. Shanghai Key Laboratory for Contemporary Applied Mathematics. School of Mathematical Sciences, Fudan University, Shanghai, 200433, China

    Zong-min Wu & Li-min Ma

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  1. Zong-min Wu
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  2. Li-min Ma
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Correspondence to Zong-min Wu.

Additional information

Supported by the 973program-2006CB303102, SGST 09DZ 2272900 and NSFC No.11026089.

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Wu, Zm., Ma, Lm. Generator, multiquadric generator, quasi-interpolation and multiquadric quasi-interpolation. Appl. Math. J. Chin. Univ. 26, 390–400 (2011). https://doi.org/10.1007/s11766-011-2812-5

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  • DOI: https://doi.org/10.1007/s11766-011-2812-5

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