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首页> 外文期刊>Journal of Computational Physics >A high order multivariate approximation scheme for scattered data sets
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A high order multivariate approximation scheme for scattered data sets

机译：散乱数据集的高阶多元逼近方案

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摘要

We present a high order multivariate approximation scheme for scattered data sets. Each data point is represented as a Taylor series, and the high order derivatives in the Taylor series are treated as random variables. The approximation coefficients are then chosen to minimize an objective function at each point by solving an equality constrained least squares. The approximation is an interpolation when the data points are given as exact, or a nonlinear regression function when nonzero measurement errors are associated with the data points. Using this formulation, the gradient information on each data point can be used to significantly reduce the approximation error. All parameters of the approximation scheme can be computed automatically from the data points. An uncertainty bound of the approximation function is also produced by the scheme. Numerical experiments demonstrate that although this method is more computationally intensive than traditional methods, it produces more accurate approximation functions.
机译：我们为分散的数据集提出了一种高阶多元逼近方案。每个数据点都表示为泰勒级数，泰勒级数中的高阶导数被视为随机变量。然后选择近似系数，以通过求解等式约束的最小二乘法来最小化每个点的目标函数。当精确给出数据点时，近似值是插值;当非零测量误差与数据点相关时，近似值是非线性回归函数。使用这种公式，可以使用每个数据点上的梯度信息来显着降低近似误差。可以根据数据点自动计算近似方案的所有参数。该方案还产生了逼近函数的不确定范围。数值实验表明，尽管该方法比传统方法具有更高的计算强度，但它产生的精度更高。

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