A univariate quasi-multiquadric interpolationwith better smoothness
A univariate quasi-multiquadric interpolationwith better smoothness
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DOI：
10.1016/j.camwa.2003.05.014
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发表时间：
2004-09
影响因子：
2.9
通讯作者：
Leevan Ling
中科院分区：
文献类型：
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作者：
Leevan Ling
本文提出了一种基于多二次基的多级单变量拟插值格式。它是实用的，因为它不需要被插值的函数的导数值。它具有比原始0级公式更高的平滑度，因为它允许形状参数c=O（h）。我们的1级准插值的设置成本为O（nlog n）次浮点运算。它保持严格的凸性和单调性。当c=O（h）时，我们证明了所提出的格式以O（h2.5log h）的速度收敛。|（a）|和|ƒ″|相对较小，收敛速度会提高。我们数值验证，c = h是一个很好的形状参数用于我们的方法，因此我们不需要找到最佳参数。对于所有测试函数，收敛速度和误差都在0.5h和1.5h之间的c下进行了优化。我们的方法可以推广到一个多层次的计划，我们包括2级计划的数值结果。Level-2格式的形状参数可在2 ~ 3 h之间选择。
In this paper, we propose a multilevel univariate quasi-interpolation scheme usingmultiquadric basis. It is practical as it does not require derivative values of the function being interpolated. It has a higher degree of smoothness than the original level-0 formula as it allows a shape parameter c=O(h). Our level-1 quasi-interpolation costs O(nlogn) flops to set up. It preserves strict convexity and monotonicity. When c=O(h), we prove the proposed scheme converges with a rate of O(h2.5logh).Furthermore, if both |ƒ″(a)| and |ƒ″| are relatively small compared with ‖ƒ″‖∞, the convergence rate will increase. We verify numerically that c = h is a good shape parameter to use for our method, hence we need not find the optimal parameter. For all test functions, both convergence speed and error are optimized for c between 0.5h and 1.5h. Our method can be generalized to a multilevel scheme; we include the numerical results for the level-2 scheme. The shape parameter of the level-2 scheme can be chosen between 2h to 3h.