# American Institute of Mathematical Sciences

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

 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.
Citation: Uwe Schäfer, Marco Schnurr. A comparison of simple tests for accuracy of approximate solutions to nonlinear systems with uncertain data. Journal of Industrial & Management Optimization, 2006, 2 (4) : 425-434. doi: 10.3934/jimo.2006.2.425
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