一族变型Halley迭代方法的收敛性

Convergence of a family of the deformed Halley iterations

研究了Banach空间中求解非线性算子方程的一族带参数的变型Halley迭代方法的收敛性问题;在二阶导数满足H lder条件下建立了它的半局部的收敛性定理及误差估计.

The convergence problem of a family of the deformed Halley iterations with parameters for solving nonlinear operator equations in Banach spaces was studied. Under the assumption that the two derivative of an operator satisfied the HOlder condition, the semi-local convergence of the deformed Halley iterations were established. Finally, the corresponding error estimate was given.