稀疏线性方程组求解的逐次超松弛迭代法

Successive Over Relaxation Iteration Method to Find the Solution of Sparsity Linear Equation System

针对稀疏线性方程组求解问题,在论述迭代法离散化处理基础上,以二维热传导方程为例,导出了热传导方程离散化后线性方程组,用超松弛(SOR)迭代法对产生的稀疏线性方程组进行迭代法求解,并分析了收敛性和收敛速度.将超松弛迭代算法在计算机上实现,得出了一组与精确解较接近的数值解,验证了逐次超松弛(SOR)迭代法的精确性.

Aiming at the problem of finding the solution of sparsity linear equation systeem, on the basis of discussing the dispersed handling for iteration method, and taking two-dimensional heat conduction equation as example, the work educes the linear equation system, finds the solution with SOR iteration method, and analyzes the convergence performance and convergence speed. It realizes SOR iteration method on the computer, gets a set of numerical solution approximated to the accurate solution, and vaalidates the accuracy of SOR iteration method.