## Monotonie und Einschließung beim Brown-Verfahren.(German)Zbl 0613.65051

Fakultät für Mathematik der Universität Karlsruhe (TH). 92 S. (1986).
The method of K. M. Brown [SIAM J. Numer. Anal. 6, 560-569 (1969; Zbl 0245.65023)] is a particularly effective method for solving the equation (1) $$F(x)=0$$, where $$F: D\subseteq {\mathbb{R}}^ n\to {\mathbb{R}}^ n$$. It is shown that Brown’s method produces a monotonically decreasing sequence of iterates if F is order convex and F’(x) has a certain M- matrix structure. In many cases one then can obtain enclosures for a zero of (1) at a very low additional computational cost. These results are valid for the usual derivative free Brown’s method as well as for the analytic Brown’s method, for multi-stage and for block modifications.

### MSC:

 65H10 Numerical computation of solutions to systems of equations

Zbl 0245.65023