非线性问题线性化计算的改进  

Modification to the processing of nonlinear problems with linear fit

作　　者：王郁文[1] 梁逸曾[2] 陈启元[2] 王学文[2] 

机构地区：[1]井冈山师范学院化学系,江西吉安343009 [2]中南大学化学化工学院,湖南长沙410083

出　　处：《计算机与应用化学》2005年第4期295-300,共6页Computers and Applied Chemistry

基　　金：国家自然科学基金资助项目(50274075)

摘　　要：通过实例分析文章中指出了传统数据处理方法中非线性问题线性化计算存在的缺陷,并对这一数据处理方法进行了相应的改进使之计算结果准确可靠。改进后的非线性问题线性计算方法是,在保持各实验点数据相对权重基本不变的条件下, 对非线性函数进行线性变换,当各实验点实验误差的平方和最小时,求目标函数Q=∑F2(J1,J2…)中J1,J2,J3,…的最佳值。邻苯二甲酸、磷酸等多元弱酸各级电离常数的计算结果表明,改进后的线性化方法处理非线性问题不仅解决了某些理论上能够线性化处理但无法实现传统线性化处理方法的问题,而且该方法还避免了在非线性拟合中因初值与精确解相差过大而出现的发散问题。By studying concrete instances, it was found that there are shortcomings in the processing of nonlinear problems with traditional linear fit method. In order to obtain accurate and trustworthy results, the method was modified: the nonlinear functions were linear transformed under the relative weight factor of experimental datum for all experimental point; when the quadratic sum of experiment error for all experimental point is least, compute the most favorable values of J1, J2, and so on from the objective function Q= ∑F2(J1,J2,…) The compute results of the ionization constants of phthalic acid and phosphoric acid showed that using the modified method to process nonlinear problems not only extends the application range of linear fit, but also avoids the divergency in nonlinear fit when the difference between initial value and exact result is too large.

关 键 词：化学计量 线性拟合 非线性拟合 

分 类 号：TB99[一般工业技术—计量学]