用解线性方程组方法求三对角矩阵的逆

Find the Inverse Matrix of Tridiagonal Matrix by Sloving Systems of Linear Algebraic Equations

根据三对角矩阵的特点 ,给出一种利用解线性方程组的方法求三对角矩阵的逆矩阵的算法 .该算法有两个优点 .第一 ,运算量小 .在整个计算过程中 ,只需进行较少次的乘除运算 .第二 ,节省内存 .除原始数据外 ,只定义三个一维数组 ,而不需任何二维数组 .数值实验表明 。

In this paper, an algorithm for finding the inverse matrix of tridiagonal matrix by sloving systems of linear algebraic equations is proposed. This algorithm is got according to the peculiarity of tridiagonal matrix. Our algorithm has two advantages. First, the amount of arithmetic operation is small. The number of multiplication and division operations is a few in whole calculation. Second, memory units of computer are saved. Only three one-dimension arrays are defined during the course of calculation, while no two-dimension arrays are needed. By valuation expeiment, our algorithm is showed has high precision.