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电极电位分析中,多次标准加入法比二次标准加入法能获得更高精度的待测溶液的浓度C。因而该法的进一步研究和改进是有实际意义的。在文献[1,2,3]中,Brand等作者借用常规的非线性最小二乘法拟合其实验数据,获得了良好结果。但是该法比较复杂,使用不大方便。本文利用Nernst方程可以转化为仅有二个未知量(C_o和S)的特点,首先根据最小二乘原理,将Nernst非线性矛盾方程组转化为相容的二元非线性方程组;进而利用所选目标函数具有凸性,又方便地转化为一维优化计算,并且用0.618法获得C_o值。文
In the electrode potential analysis, the concentration C of the test solution can be obtained with higher accuracy by adding the standard multiple standard addition method to the second standard addition method. Therefore, further study and improvement of this law is of practical significance. In the literature [1,2,3], Brand et al. Obtained good results by fitting their experimental data using the conventional nonlinear least-squares method. But the law is more complicated, not easy to use. In this paper, the Nernst equation can be transformed into the characteristics of only two unknowns (C_o and S). First, according to the least squares principle, the Nernst nonlinear equations of contradiction are transformed into a compatible binary nonlinear equations. The selected objective function has convexity and is easily converted into one-dimensional optimization calculation, and the C_o value is obtained by the 0.618 method. Text