广义简化牛顿迭代收敛研究

Banach空间E的某个区域到同型空间F的Fréchet可微的算子f:E→F,A:F→E是一个相反的固定的线性算子,迭代zn+1=zn-Af(zn)为简化牛顿迭代,其中n∈N0,A=Df(z0)-1.用KaHTOPOBИЧ的区域判据和Smale的点估计判据研究广义简化牛顿迭代的收敛性和收敛域的大小,并且包括当α(f,z)≤3-2 2时广义简化Newton迭代收敛情况.

Point estimates and convergence domain on the modified Newton iteration

Let f:E→F be a Fréchet derivable map from one Banach space to anothet and A:F→E be a linear map with bounded inverse.We call the iteration zn+1=zn -Af(z n),n ∈N0,a generalized chlrd method iteration.When A=Df(z0) -1,the iteration is the modified Newton method iteration.The convergence and convergence domain by means of KaHTOPOBИЧ,s Domain criteria and Smale,s point estinate criteria are studied.It contains a special case,the modified Newton iteration convergence when α(f,z)≤3-2 2.This demonstrates that number 3-2 2 is universal for many concrete iterations.