调整右矢量的加速牛顿类迭代法

Study of accelerated Newton-like method withmodification of the right-hand-side vector

设计了一个新的牛顿类迭代方法.该迭代法设计了最佳松弛参量并不断调整线性系统的右端矢量,它比牛顿方法的计算量要少,比修正的牛顿方法收敛得快.分析了松弛参量的作用,并给出了最佳参量的计算公式.使用数值例子证明了该方法的优良性质,用衡量指数对比了其他几种迭代法,证明了该方法的优越性.

A Newton-like method was presented to design the optimal relaxation parameter and constantly adjusted the right-hand-side vector of linear system. This method was less computation than that of the Newton method and was faster than the fixed Newton method in convergence. The influence of the relaxation parameter was analyzed and the computation formulae for the optimal parameters were given. The numerical examples were used to prove the advantages of the proposed method. In comparison with other iteration methods by weighing index, the superiority of the proposed method was proved.