求解三对角线性方程组的迭代对角占优算法

摘要

In parallel solving weak diagonal dominant tridiagonal systems, the approximate error of the Parallel Diagonal Dominant (PDD) algorithm cannot be ignored. An iterated PDD algorithm was presented. In the algorithm, the solution of the correction value was calculated by iterative method, and the computational accuracy was obviously improved. Through error analysis on the algorithm, an estimation formula of iteration number was derived for a given error tolerance. And the numerical experiment shows the validity. Based on the complexity analysis of the iterative and non-iterative PDD algorithm, the increase of iterative algorithm computational complexity is very small, but the communication complexity increases exponentially with the iteration number.%针对并行求解三对角线性方程组的对角占优(PDD)算法,在系数矩阵为弱对角占优时,近似处理引入误差较大的问题,提出了一种PDD算法的迭代方案.该方案在解的修正值计算中采用迭代方法,计算精度得到了提高；通过对算法的误差分析,导出了算法在给定误差下迭代次数的估算式；数值实验说明了算法的有效性.通过对迭代与非迭代的PDD算法的复杂性分析,迭代算法的计算复杂性增加很小,但通信复杂性随迭代次数成倍增加.