INTERVAL ARITHMETIC TOOLS FOR RANGE APPROXIMA-TION AND INCLUSION OF ZEROS Summary: INTERVAL ARITHMETIC TOOLS FOR RANGE APPROXIMA- TION AND INCLUSION OF ZEROS G.ALEFELD Institut für Angewandte Mat~ematik Universität Karlsruhe 76128 Karlsruhe e-mail: goetz.alefeId@math.uni-karlsruhe.de 1. Introduction In this paper we start in section 2 with an introduction to the basic facts of interval arithmetic: We introduce the arithmetic operations, explain how the range of a given function can be included and discuss the problem of overesti- mation of the range. Finally we demonstrate how range inclusion (of the first deriva.tive of a given function) can be used to compute zeros by a so-called en- closure method. An enclosure method usually starts with an interval vector which contains a solution and improves this inclusion iteratively. The question which has to be discussed is under what conditions is the sequence of including interval vectors convergent to the solution. This will be discussed in section 3 for so-called Newton-like enclosure methods. An interesting feature of inclusion methods is that they cau also be used to prove tha.t there exists no solution in an interval Collections: Mathematics