用插值法求拟三对角方程组的数值解

Method of Interpolation for the Numerical Solution of Quasi-Tridiagonal System of Linear Equations

文章将求解三对角线性方程组数值解的插值法进行推广 ,得到一种求解拟三对角方程组的插值算法 .从理论分析和数据实验两方面都表明 ,此算法的时间复杂性和精度都与LU分解法相当 .由于在计算过程中不需设置二维数组 ,和其它算法比较起来 ,它占有较小的内存 .另外 ,此算法的设计思想还可用来求解其它一些线性方程组 .

In this paper,the method of interpolation for the numerical solution of tridiagonal system of linear equations is popularized,and another method of interpolation for quasi-tridiagonal system of linear equations is proposed. It can be seen that both the time complexity and precision are matched with those of LU resolving method through theory analysis and data experiment. Our algorithm occupies less Memory than other algorithms because it needs no two-dimension data during the whole calculation. The design method in this paper can also be used to solve some other systems of linear equations.