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What are 'Good' Points for Local Interpolation by Radial Basis Functions.

机译：什么是径向基函数局部插值的“好”点。

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Radial basis function interpolation has an advantage over other methods in that the interpolation matrix is nonsingular under very weak conditions on the location of the interpolation points. However, we show that point location can have a significant effect on the performance of an approximation in certain cases. Specifically, we consider multiquadric and thin plate spline interpolation to small data sets where derivative estimates are required. Approximations of this type are important in the motion of unsteady interfaces in fluid dynamics. For data points in the plane, it is shown that interpolation to data on a circle can be related to the polynomial case. For scattered data on the sphere, a comparison is made with the results of Sloan and Womersley.

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Tong, R. P.; Crampton, A.; Trefethen, A. E.;
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年度 2001
页码 1-9
总页数 9
原文格式 PDF
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关键词
Interpolation; Special functions(Mathematics); Algorithms; Symposia; Approximation(Mathematics); Polynomials; Functional analysis; Fluid dynamics; Curve fitting; United kingdom; Component report; Foreign reports; Radial basis functions;

机译：插值;特殊函数（数学）;算法;专题讨论会;近似（数学）;多项式;功能分析;流体动力学;曲线拟合;英国;组件报告;外国报告;径向基函数;

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3. Local radial basis function interpolation method to simulate 2D fractional-time convection-diffusion-reaction equations with error analysis [J] . Shivanian Elyas Numerical Methods for Partial Differential Equations: An International Journal . 2017,第3期

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What are 'Good' Points for Local Interpolation by Radial Basis Functions.

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