一种改进的求解大型线性方程组的Jacobi迭代法

A modified Jacobi iterative method for large-size linear systems

针对求解大型线性方程组提出了一种新的Jacobi迭代法。其思想是用Jacobi迭代法得到的当前点和上一步迭代点的组合得到下一步迭代点,并且通过求解最小二乘优化问题求得最佳组合因子。在与经典的Jacobi迭代法相同的条件下,证明了这种最优外插Jacobi迭代法的全局收敛性,进一步的数值实验也验证了新算法的有效性。

An improved Jacobi method is proposed for solving large-size linear system.The improvement of the proposed method is to use the combination of the current point obtained by Jacobi method and the previous point to get the new point,to get the optimal factor of linear combination by solving the least square optimization.Under the same conditions as the classic Jacobi method,the global convergence of this method is proved,the computational results show the effectiveness of this method.