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Stochastic arithmetic has been developed as a model for exact
computing with imprecise data. Stochastic arithmetic provides confidence
intervals for the numerical results and can be implemented in any existing
numerical software by redefining types of the variables and overloading the
operators on them. Here some properties of stochastic arithmetic are further
investigated and applied to the computation of inner products and the
solution to linear systems. Several numerical experiments are performed
showing...
Control strategies for nonlinear dynamical systems often make use of special system properties, which are, for example, differential flatness or exact input-output as well as input-to-state linearizability. However, approaches using these properties are unavoidably limited to specific classes of mathematical models. To generalize design procedures and to account for parameter uncertainties as well as modeling errors, an interval arithmetic approach for verified simulation of continuoustime dynamical...
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