求拟反三对角线性方程组的一种数值方法

A Numerical Method for Solving the Proposed Antitridiagonal Linear Equations

通过分析拟反三对角线性方程组的结构,结合求解对角线性方程组的插值法,提出了一种求解拟反三对角线性方程组的插值算法,从而推广了用于求对角线性方程组数值解的插值法.它占有较小的内存,作为直接法不需要考虑收敛性,其解也只有舍入误差.此算法具有比较快的计算速度和高的精度,程序编写简单,具有可行性.

By analyzing the structure of the proposed anti-tridiagonal linear equations, and in combination with the inter- polation method used in solving diagonal linear equations, a new interpolation algorithm is proposed for solving anti-tridiagonal linear equations, which popularizes the interpolation method used to seek diagonal linear equations numerical solutions. Com- pared with the traditional algorithm, this method takes less memory. It occupied less memory, besides, as a direct method, consideration of convergence did not be required. At the same time, for the solution, there was only a rounding error. This algortihm has not only faster computing speed but high accuracy. Programming is simple and in practical applications, this algortihm is feasible.