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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

  

Source: Alefeld, Götz - Institut für Angewandte und Numerische Mathematik & Fakultät für Mathematik, Universität Karlsruhe

 

Collections: Mathematics