Abstract
We compare two computational tests for the existence of a zero of a nonlinear system. One of the tests is based on a theorem by Moore, the other relies on Miranda’s theorem. It turns out that the Miranda test is always at least as powerful as the Moore test. We also indicate some conditions under which both tests are equivalent.
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B. Lang gratefully acknowledges support by VolkswagenStiftung within the project “Konstruktive Methoden der Nichtlinearen Dynamik zum Entwurf verfahrenstechnischer Prozesse”, Geschäftszeichen I/79 288.
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Frommer, A., Lang, B. & Schnurr, M. A Comparison of the Moore and Miranda Existence Tests. Computing 72, 349–354 (2004). https://doi.org/10.1007/s00607-004-0064-4
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DOI: https://doi.org/10.1007/s00607-004-0064-4
Keywords
- Nonlinear systems
- Moore’s theorem
- Miranda’s existence theorem
- computational verification
- interval analysis