杜利特尔算法在条件优化中的应用

The application of Doolittle algorithm in condition optimization

杜利特尔算法作为1种高精密度低计算量的数值分析法,在数学等诸多领域得到了广泛的应用,但在分析化学方面的应用则不多见。这种算法通过三角分解矩阵、降阶,简化矩阵运算而实现,与传统多元校正法相比具有更高的灵敏度。本文首次将杜利特尔法引入分析化学中的条件优化,以影响色谱分离度的3个因素为例,均匀实验设计癸烷和十二烷烃体系分离,得到分离度范围为50.124 2～98.694 2的不同实验体系,而后分别运用杜利特尔法和经典的最小二乘法建立的回归方程拟合实验结果,结果表明运用杜利特尔法所得出回归方程的拟合误差仅为-2.50%～2.61%,明显优于最小二乘法的结果(-24.67%～-57.47%)。说明杜利特尔多元校正法运用于条件优化方面比较理想,所拟合出的回归方程可以直接预测和推算实验条件的优劣性,在分析化学中具有广泛的应用前景。

Doolittle algorithm, which has been applied in many aspects such as math, computer, electronics and so on, is a numerical analysis method with high accuracy and low cost. It is implemented by LU decomposition of the matrix which can predigest the matrix operation and is more precise than other multivariate calibration methods. In this paper, Doolittle algorithm was introduced into the field of condition optimization of analytical chemistry firstly. The chromatography separation conditions of decane and 12-alkanes were difficult to obtain. Uniform design was applied to the new system of three factors that effect resolution in chromatography. Different experiment systems with resolutions from 50. 124 2 to 98. 694 2 were got. Multiple regression equation was got by using Doolittle multivariate calibration method and least squares （LS） respectively. Then, experiment data were validated by both equations. The result shows that Doolittle method is superior to IS. The relative standard deviation of Doolittle algorithm is from - 2. 50% to 2. 61%, while that of IS is from - 24. 67% to - 57.47% . It is demonstrated that Doolittle algorithm is effective in condition optimization and the multiple regression equation got by Doolittle algorithm can be used to predict whether the experiment condition is good or not.