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

Abstract

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.