Abstract
We propose an arithmetic of function intervals as a basis for convenient rigorous numerical computation. Function intervals can be used as mathematical objects in their own right or as enclosures of functions over the reals. We present two areas of application of function interval arithmetic and associated software that implements the arithmetic: (1) Validated ordinary differential equation solving using the AERN library and within the Acumen hybrid system modeling tool. (2) Numerical theorem proving using the PolyPaver prover. © 2014 Springer-Verlag.
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Duracz, J., Farjudian, A., Konečný, M., & Taha, W. (2014). Function interval arithmetic. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 8592 LNCS, pp. 677–684). Springer Verlag. https://doi.org/10.1007/978-3-662-44199-2_101
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