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.
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Goldsztejn, A. Comparison of the Hansen-Sengupta and the Frommer-Lang-Schnurr existence tests. Computing 79, 53–60 (2007). https://doi.org/10.1007/s00607-006-0217-8
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DOI: https://doi.org/10.1007/s00607-006-0217-8