系数成三对角阵方程的新解法及其应用

A New Method of Solving the Diagonally Coefficient Tridiagonal Matrix Equation and Its Application

利用行列式和矩阵的基本性质,对方程系数矩阵进行改造,达到压缩降阶的效果,一个高阶矩阵通过降阶后可以变成两阶矩阵,从而可方便方程求解,同时得到了三对角矩阵行列式的另一求法,尤其适用于多跨变截面连续梁的求解。

This paper reforms the equation coefficient matrix to achieve reduction of order according to the basic proper- ties of determinant and matrix; a higher order matrix can be changed to a two- order matrix by means of reduction of or- der so that it is convenient to solve the equation. Meanwhile, the paper has obtained another method of solving the tridi- agonal matrix determinant, which is particularly applicable to solution of a continuous muhispan beam with varying cross sections.