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首页> 外文期刊>Journal of Computational and Applied Mathematics >A Newton-type method for constrained least-squares data-fitting with easy-to-control rational curves
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A Newton-type method for constrained least-squares data-fitting with easy-to-control rational curves

机译：具有易于控制的有理曲线的约束最小二乘数据拟合的牛顿型方法

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摘要

While the mathematics of constrained least-squares data-fitting is neat and clear, implementing a rapid and fully automatic fitter that is able to generate a fair curve approximating the shape described by an ordered sequence of distinct data subject to certain interpolation requirements, is far more difficult. The novel idea presented in this paper allows us to solve this problem with efficient performance by exploiting a class of very flexible and easy-to-control piecewise rational Hermite interpolants that make it possible to identify the desired solution with only a few computations. The key step of the fitting procedure is represented by a fast Newton-type algorithm which enables us to automatically compute the weights required by each rational piece to model the shape that best fits the given data. Numerical examples illustrating the effectiveness and efficiency of the new method are presented. (C) 2008 Elsevier B.V. All rights reserved.
机译：虽然受约束的最小二乘数据拟合的数学方法是简洁明了的，但要实现一种快速，全自动的拟合器，该方法能够生成近似曲线，该近似曲线受特定插值要求的不同数据的有序序列所描述的形状的影响，目前还远远不够。更加困难。本文提出的新颖思想使我们能够通过利用一类非常灵活且易于控制的分段有理Hermite插值来高效地解决此问题，该插值使得仅需进行少量计算即可确定所需的解决方案。快速牛顿型算法代表了拟合过程的关键步骤，该算法使我们能够自动计算每个有理零件所需的权重，以对最适合给定数据的形状进行建模。数值例子说明了新方法的有效性和效率。 （C）2008 Elsevier B.V.保留所有权利。

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