大范围求解非线性方程的加速迭代法

An accelerated iteration solution to nonlinear equation in large scope

为了解决一些传统方法不能解决的非线性方程求根问题,提出一种大范围求解的加速迭代法,利用卷积实现了大范围内选用初值,并加速过渡到根的邻域中,由于在局部迭代求根的过程中采用了松弛参数,局部迭代过程得到加速,加速效果非常明显.相关算例显示这种加速迭代算法不仅能在大范围内选取初值,不用计算导数,而且计算量和迭代步数少,收敛速度快,计算精度高.

An accelerated iteration method used in large-scope solution was put forward to deal with nonlinear equations which were not solved by some traditional methods. The initial value was chosen in large scope and accelerated to pass through to the neighbor of the root by convolution. The relaxation parameters were adapted in the course of extracting a root at the part iteration to accelerate the part iteration obviously. The relevant examples showed that the proposed method could choose the initial value in large scope, without computing differential coefficient and iteration steps, and less computation with high precision and fast convergence speed.