Generalized least-squares fit of multiequation models
Generalized least-squares fit of multiequation models
复制标题
多重方程模型的广义最小二乘拟合
DOI：
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发表时间：
2005
期刊：
影响因子：
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通讯作者：
J. Blencoe
中科院分区：
文献类型：
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作者：
S. Marshall;J. Blencoe
提出了一种将多方程模型拟合到有限精度数据集的方法。这是基于 Britt 和 Luecke (1973) 设计的高斯-牛顿算法；包含每个数据点要满足的几个条件方程会产生有效加权矩阵的块对角形式。该方法允许对函数进行广义非线性最小二乘拟合，这些函数更容易以参数形式 (x(t),y(t)) 表示，而不是以 y=f(x) 形式的显式函数关系表示。在自变量的方差和协方差为零的极限情况下，恢复了适用于多方程加权非线性最小二乘法的 Aitken (1935) 公式。详细讨论了与此类计算性能相关的实际考虑因素，例如所需偏导数和矩阵乘积的评估，并通过将其应用于复介电常数数据与 D 的拟合来说明算法的操作。
A method for fitting multiequation models to data sets of finite precision is proposed. This is based on the Gauss–Newton algorithm devised by Britt and Luecke (1973); the inclusion of several equations of condition to be satisfied at each data point results in a block diagonal form for the effective weighting matrix. This method allows generalized nonlinear least-squares fitting of functions that are more easily represented in the parametric form (x(t),y(t)) than as an explicit functional relationship of the form y=f(x). The Aitken (1935) formulas appropriate to multiequation weighted nonlinear least squares are recovered in the limiting case where the variances and covariances of the independent variables are zero. Practical considerations relevant to the performance of such calculations, such as the evaluation of the required partial derivatives and matrix products, are discussed in detail, and the operation of the algorithm is illustrated by applying it to the fit of complex permittivity data to the D...