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October  2006, 2(4): 425-434. doi: 10.3934/jimo.2006.2.425

A comparison of simple tests for accuracy of approximate solutions to nonlinear systems with uncertain data

Uwe Schäfer 1, and  Marco Schnurr 1,

1. 

Institut für Angewandte und Numerische Mathematik, Universität Karlsruhe, 76128 Karlsruhe, Germany, Germany

Received  January 2006 Revised  August 2006 Published  October 2006

Recently, Frommer, Lang, and Schnurr [4] presented an existence test, which can be used to prove the existence of a zero of a continuous mapping from $\R^n $ to $\R^n$. The existence test relies on Miranda's theorem and was shown to be more powerful than the Moore test [10]. In this paper, we show that under additional assumptions, the Moore and Kioustelidis test [11] can be applied successfully in more cases than that of Frommer, Lang, and Schnurr [4]. For instance, these assumptions are fulfilled concerning the linear complementarity problem with interval data.
Keywords: nonlinear systems, Miranda's theorem, linear complementarity problem., Moore test, optimal enclosure, Computational verification.
Mathematics Subject Classification: 47H10, 65G20, 65G40, 65H10, 90C3.
Citation: Uwe Schäfer, Marco Schnurr. A comparison of simple tests for accuracy of approximate solutions to nonlinear systems with uncertain data. Journal of Industrial and Management Optimization, 2006, 2 (4) : 425-434. doi: 10.3934/jimo.2006.2.425
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