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.
This work was supported by EPSRC grant EP/C01037X/1, Altran Technologies SA, the US NSF CPS award 1136099 and Swedish KK-Foundation CERES Centre.
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Duracz, J., Farjudian, A., Konečný, M., Taha, W. (2014). Function Interval Arithmetic. In: Hong, H., Yap, C. (eds) Mathematical Software – ICMS 2014. ICMS 2014. Lecture Notes in Computer Science, vol 8592. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44199-2_101
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DOI: https://doi.org/10.1007/978-3-662-44199-2_101
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