二步迭代法在中心仿射Hlder条件下的收敛性

Convergence analysis of the two-step combined method under center affine Hlder condition

研究了Banach空间中非线性算子方程的求解问题,在一阶Fréchet导数和二阶Fréchet导数分别满足L平均中心仿射Hlder条件和L平均Lipschitz条件下,讨论了二步迭代法的局部收敛性,得到了局部收敛性的条件,同时证明了该方法的R收敛阶至少是1+p/2+(1+p)24+p2.

Under the center affine H lder condition with L average and the Lipschitz condition with L average for the first and second Fr chet derivatives,respectively,the local convergence of a two-step combined method for solving nonlinear operator equations was studied.Some local convergence was given,the R order of convergence was proved to be at least 1+p[]2+(1+p)\+2[]4+p\+2 under these conditions.