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Function interval arithmetic. (English) Zbl 1435.65071
Hong, Hoon (ed.) et al., Mathematical software – ICMS 2014. 4th international congress, Seoul, South Korea, August 5–9, 2014. Proceedings. Berlin: Springer. Lect. Notes Comput. Sci. 8592, 677-684 (2014).
Summary: 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.
For the entire collection see [Zbl 1293.65003].
MSC:
65G30 Interval and finite arithmetic
Software:
AERN; iRRAM; PolyPaver
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