多元非线性数据拟合模型的数学推论及其回归方程的计算机拟合

Inference of Mathematical Model of Fitting Multiple Nonlinear Data and Its Regression Fitting by Computer

本文推论了多元非线性数据拟合的通用数学模型,利用最小二乘法和极值原理,导出求解多元非线性回归方程的规范方程组。并用矩阵形式对规范方程组进行表述,在所表述的诸矩阵中,结构矩阵是其基础。用它可方便地转化出其他矩阵,这将大大简化程序的编制和规范方程组的解算。计算机根据输入数据自变量的个数和实验所作次数的多少,求解出相应的多元非线性回归方程及其评估方程质量的数据。

In this paper, common mathematical model of multiple nonlinear data fitting is inferred. A set of normal equations is deduced from using the method of least squares and minimum theory and so is expressed in a matrix form. The structural matrix transforms into other matrix very easily. It can be used to simplify program design and calculation of the set of normal equations. According to the number of independent variables the corresponding multiple nonlinear regressive equation is fitted out and the data of its assessment is put out.