Ein Einschließungsverfahren für Nullstellen

In this paper we give a method for determining the zeros of a function or a system of functions in an arbitrary given region B. Applying this method we need no approximations of the zeros. Further we need no preliminary knowledge of the order and the number of the zeros in B. Against this our method is based on a suitable "estimation" of the function or the system of functions. We show that the simple interval arithmetic for rational functions gives such estimations. As result the zeros are included by upper and lower bounds. The accuracy of the results depends only on the number of digits of the computer. The method was tested on many examples, some of which are given below. © 1967 Springer-Verlag.