Proving the existence of zeros using the topological degree and interval arithmetic

Authors:
A. Frommer;F. Hoxha;B. Lang
Affiliations:
Bergische Universitát Wuppertal, Applied Computer Science and Scientific Computing, Wuppertal, Germany;Department of Mathematics, Faculty of Natural Sciences, University of Tirana, Tirana, Albania;Bergische Universitát Wuppertal, Applied Computer Science and Scientific Computing, Wuppertal, Germany
Venue:
Journal of Computational and Applied Mathematics - Special issue: Scientific computing, computer arithmetic, and validated numerics (SCAN 2004)
Year:
2007

Citing 3
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Abstract

The invariance of the topological degree under certain homotopies is used to computationally prove the existence of zeros of nonlinear mappings in Rn. These existence tests use interval arithmetic to enclose the range of a function over a box. We show that our test is more general than a well-known test based on Miranda's theorem, and we show by a numerical example that the new test can be successful on substantially larger boxes.