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本文讨论了用线性方程组和最小二乘法进行数据处理的问题。用Gram法则对这两种方法进行了误差分析,由此得到的误差关系式意义明确,不存在过估问题,并可用于简化计算和选择最佳测量点。我们使用模拟变换方法解决最小二乘非负约束问题并编制了正交法和改进的Newton最小二乘法的FORTRAN通用计算程序。这个方法被用于铌钽和铌钽钒体系的同时光度测定。免去了铌钽共存时所需的色层和萃取分离。前者已用于合金钢样中铌钽的同时测定,方法的总变动系数0.021(n=17);后者用于合成样中铌钽钒的同时测定,使用pH1.4和3.0两个条件,方法的总变动系数0.054(n=36)。
This article discusses the problem of using linear equations and least squares for data processing. The errors of these two methods are analyzed by Gram’s rule. The error relation obtained by this method has clear meaning, no over-estimation problem, and can be used to simplify the calculation and choose the best measurement point. We use the method of analogue transformation to solve the problem of least squares nonnegative constraints and develop the FORTRAN generalized calculation program of orthogonal method and improved Newton least square method. This method is used for the simultaneous photometric determination of niobium tantalum and niobium tantalum vanadium systems. Eliminating the need for the coexistence of niobium and tantalum chromatography and extraction separation. The former has been used for simultaneous determination of niobium and tantalum in alloy steel samples. The total variation coefficient of the method is 0.021 (n = 17). The latter is used for the simultaneous determination of vanadium niobium tantalum and vanadium in the composite samples. The total coefficient of variation of the method is 0.054 (n = 36).