关于非线性方程的单调Steffensen型迭代法

ON THE STEFFENSEN-LIKE MONOTONE ITERATION FOR NONLINEAR EQUATIONS

本文引进一类重要的非凸算子——可凸分解算子的概念,并对可凸分解算子类讨论了一般化的 Steffensen 型单调包含迭代法.作者证明:在通常假设下,所引进的 Steffensen 型单调迭代法至少平方收敛到所考虑算子方程的极小解和极大解.所得结果包含并推广了有关单调 Newton 法和单调 Steffensen 方法的已知结果.数值例题说明,本文所引进的 Steffensen 型方法在计算上是非常有效的,因而值得推荐.

This paper introduces a class of nonconvex operators-convex^1ydecomposable operators,for which the generalization of Steffensen-like monotonic inclusive iteration methods for operator equations is discussed.Under some usual assumptions,it is shown that these methods converge to the maximum and mini- mum solutions of equtions,and the convergence is at least quadrati c,the theo- rems obtained in the paper generalize and unify many known results about monotone convergence of Newton's method and Steffensen method.Some nume- rical examples are given.