矩阵前主子式的三角分解改进  

Matrix Triangular Decomposition Improvement of Pre Order Principal Sub Determinant

作　　者：苏尔[1] 

机构地区：[1]浙江传媒学院新媒体学院,杭州310018

出　　处：《计算机科学》2017年第B11期148-153,共6页Computer Science

摘　　要：采用部分主元素的Gauss消去法一般不能得到矩阵的各阶前主子式。讨论围绕逐步约化的细分每小步,对一个经过若干行置换后的A_0最后实现三角分解,并且依顺序求出A_0各阶前主子式。主要内容是对带有行交换三角形化的通常约化方法实现改进,并以代数表示式结合矩阵乘积运算的递推方法,归纳证明最后约化结果式子为矩阵L-U三角分解的实现依据。逐步约化步骤的同时得到原有矩阵A_0的各阶前主子式。Using Gauss elimination method with part main elements is generally not got all principal sub determinants of matrix. This article discussed around gradual reduction with each step-by-step subdivision, final triangular decomposi-tion was performed on matrix Ao by row permutation after a number of row replacement, and each pre order principal sub determinant of Ao was found out orderly. Main purpose of the article is to achieve improvement for usually triangle reduction method by row permutation, with a recursive method for algebraic representation, to bind matrix product opration, and it inductively proves that final reduction result is in accordance with the realization of the L-U triangular de-composition to matrix. And at the same time with the process of gradual reduction, we got all pre order principal sub de-terminants of original matrix A0 .

关 键 词：行置换 逐步约化 三角分解 前主子式 矩阵运算 

分 类 号：O241.6[理学—计算数学]