Computing

, Volume 79, Issue 1, pp 53–60 | Cite as

Comparison of the Hansen-Sengupta and the Frommer-Lang-Schnurr existence tests

Article

Abstract

The Krawczyk and the Hansen-Sengupta interval operators are closely related to the interval Newton operator. These interval operators can be used as existence tests to prove existence of solutions for systems of equations. It is well known that the Krawczyk operator existence test is less powerful that the Hansen-Sengupta operator existence test, the latter being less powerful than the interval Newton operator existence test. In 2004, Frommer et al. proposed an existence test based on the Poincaré-Miranda theorem and proved that it is more powerful than the Krawczyk existence test. In this paper, we complete the classification of these four existence tests showing that, in practice, the Hansen-Sengupta existence test is actually more powerful than the existence test proposed by Frommer et al.

AMS Subject Classifications

65H10 65G20 65G40 

Keywords

Nonlinear systems of equations existence test interval analysis 

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Copyright information

© Springer-Verlag Wien 2007

Authors and Affiliations

  1. 1.Information and Computer ScienceUniversity of CaliforniaIrvineUSA

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