类Vandermonde矩阵的LU分解及其行列式值  

LU Factorization of Vandermonde-like Matrices and Their Determinant Values

作　　者：池增增 郑德印 CHI Zengzeng;ZHENG Deyin(School of Mathematics,Hangzhou Normal University,Hangzhou 311121,China)

机构地区：[1]杭州师范大学数学学院,浙江杭州311121

出　　处：《杭州师范大学学报(自然科学版)》2025年第2期204-212,共9页Journal of Hangzhou Normal University(Natural Science Edition)

摘　　要：矩阵LU分解可以通过Gauss消元法实现,考虑不交换行的Gauss消元过程,使用差商建立迭代过程中发生函数的递推公式,通过引入完全初等对称函数,给出3种类型的类Vandermonde矩阵分解的L矩阵、U矩阵和逆矩阵的显式表达,以及它们的行列式值,同时也引出了2组广义平移阶乘之间的一对反演关系.Matrix LU factorization can be implemented by Gauss elimination method.By applying difference quotient,the paper established the recursive formula of generating functions in the iterative process while considering Gauss elimination process without row exchanges.By introducing the complete elementary symmetry function,the explicit expressions of L matrix, U matrix and inverse matrix of three types of Vandermonde-like matrix factorizations were given,as well as their determinant values,and a pair of inversion relation between the two sets of generalized shifted factorials was also introduced.

关 键 词：类Vandermonde矩阵 矩阵LU分解 完全初等对称函数 行列式 差商 

分 类 号：O241.3[理学—计算数学]