两类五对角行列式的计算研究  

Determinant of Two Types of Five-Diagonal Matrices

作　　者：韩摩西 张伟 胡卫敏 HAN Moxi;ZHANG Wei;HU Weimin(School of Mathematics and Statistics,Yili Normal University,Yining 835000,China;Institute of Applied Mathhematics,Yili Normal University,Yining 835000,China)

机构地区：[1]伊犁师范大学数学与统计学院,新疆伊宁835000 [2]伊犁师范大学应用数学研究所,新疆伊宁835000

出　　处：《长春师范大学学报》2024年第8期1-7,共7页Journal of Changchun Normal University

基　　金：伊犁师范大学校级科研项目“带有时延的离散多智能体系统的一致性问题”(2022YSPY002)。

摘　　要：五对角行列式的求解问题在偏微分方程的数值求解、图像处理、电路分析、生物信息学等方面具有非常广泛的应用.本文将两类五对角行列式通过Laplace展开,将各余子式与其自身表示为一阶线性递推方程组,在此基础上将行列式随阶数变化的值表示为系数矩阵的幂方与初值向量乘积的形式.并通过LU分解将两类行列式的值表示为二元递推方程组的解的连乘积的形式.The value of five-diagonal determinants has very broad applications in numerical solutions of partial differential equations,image processing,circuit analysis,and bioinformatics.Firstly,in this paper,the two types of five-diagonal determinants are expanded through Laplace,and each cofactor and itself are represented as the solution of a first-order linear recursive equation system.Further,the values of the determinant are represented as the product of the power of the coefficient matrix and the initial value vector.Secondly,the values of the two types of determinants are represented as the continuous product of the solutions of the binary recursive equation system through LU decomposition.

关 键 词：五对角行列式 递推方程 LU分解 

分 类 号：O175.8[理学—数学]