Construction techniques for multivariate modified quasi-interpolants with high approximation order
Construction techniques for multivariate modified quasi-interpolants with high approximation order
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DOI：
10.1016/j.camwa.2012.10.006
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发表时间：
2013
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影响因子：
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通讯作者：
D. Barrera;A. Guessab;M. Ibáñez;O. Nouisser
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文献类型：
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作者：
D. Barrera;A. Guessab;M. Ibáñez;O. Nouisser
本文提出了非均匀数据上多元函数的几种拟插值逼近方法，并研究了它们的性质。特别地，我们通过单位分解的方法来刻画那些保持常量的。作为主要结果之一，我们展示了如何通过对给定的拟插值项进行非常简单的修改来构造具有显著性质的新的拟插值项。我们还给出了关于二元C~2五次样条拟插值的一些结果。最后，通过数值试验验证了这些拟插值项的逼近能力。
In this paper, we propose several approximations of a multivariate function by quasi-interpolants on non-uniform data and we study their properties. In particular, we characterize those that preserve constants via the partition of unity approach. As one of the main results, we show how by a very simple modification of a given quasi-interpolant it is possible to construct new quasi-interpolants with remarkable properties. We also provide some results regarding bivariate C2quintic spline quasi-interpolation. Finally, numerical tests are presented to show the approximation power of these quasi-interpolants.