Computing the determinant of a matrix with the univariate and multivariate polynomial entries arises frequently in the scientific computing and engineering fields. This paper proposes an effective algorithm to compute...Computing the determinant of a matrix with the univariate and multivariate polynomial entries arises frequently in the scientific computing and engineering fields. This paper proposes an effective algorithm to compute the determinant of a matrix with polynomial entries using hybrid symbolic and numerical computation. The algorithm relies on the Newton＇s interpolation method with error control for solving Vandermonde systems. The authors also present the degree matrix to estimate the degree of variables in a matrix with polynomial entries, and the degree homomorphism method for dimension reduction. Furthermore, the parallelization of the method arises naturally.展开更多
文摘采用近红外(Near Infrared,NIR)技术(12500~5400cm^(-1))快速无损检测牛肉糜的掺假。判别分析(Discriminant Analysis,DA)、主成分回归(Principle Component Regression,PCR)等功能强大的化学计量学技术被用于掺假检测和掺假水平预测模型。通过选择适当的光谱波长和使用不同的光谱预处理方法,优化了DA和PCR模型。选择特定波长和使用(无预处理方法)的DA模型分类率达到了100%。基于全波长和使用(无预处理方法的)PCR的最佳预测模型的相关系数Rp为92.21%,样本的预测均方根误差(Root Mean Square Error Of Prediction,RMSEP)为9.80。研究结果说明NIR技术对牛肉糜的掺假体系适用。
基金supported by China 973 Project under Grant No.2011CB302402the National Natural Science Foundation of China under Grant Nos.61402537,11671377,91118001China Postdoctoral Science Foundation funded project under Grant No.2012M521692
文摘Computing the determinant of a matrix with the univariate and multivariate polynomial entries arises frequently in the scientific computing and engineering fields. This paper proposes an effective algorithm to compute the determinant of a matrix with polynomial entries using hybrid symbolic and numerical computation. The algorithm relies on the Newton＇s interpolation method with error control for solving Vandermonde systems. The authors also present the degree matrix to estimate the degree of variables in a matrix with polynomial entries, and the degree homomorphism method for dimension reduction. Furthermore, the parallelization of the method arises naturally.
