关于可凸分解算子方程单调Steffensen型迭代法的进一步研究(为庆贺游兆永教授60寿辰而作)

Further Study of Stcffcnscn-like Monotone Iteration for Convex-DecomposableOperator Equation

本文是文[6]工作的继续,给出了可凸分解算子的若干实用判别准则。特别,证明了一个算子若其二阶导算子有界,则必是可凸分解算子.本文并给出了可凸分解算子方程Steffensen型迭代的若干具体化算法。

In this paper we continue studing the stcffensen-like monotone iteration. We give two efficient criter-ions of convex-decomposabe operator, and show that, if an operator has bounded second derivative, it must be convex-decomposable operator. We also give some substantial methods of steffensen-like iteration.