Abstract
We present a framework for validated numerical computations with real functions. The framework is based on a formalisation of abstract data types for basic floating-point arithmetic, interval arithmetic and function models based on Banach algebra. As a concrete instantiation, we develop an elementary smooth function calculus approximated by sparse polynomial models. We demonstrate formal verification applied to validated calculus by a formalisation of basic arithmetic operations in a theorem prover. The ultimate aim is to develop a formalism powerful enough for reachability analysis of nonlinear hybrid systems.
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Acknowledgments
Helpful discussions with Mioara Joldeş and Rolland Zumkeller are acknowledged. The second author was supported by a VENI Grant from The Netherlands Organisation for Scientific Research (NWO).
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Collins, P., Niqui, M. & Revol, N. A Validated Real Function Calculus. Math.Comput.Sci. 5, 437–467 (2011). https://doi.org/10.1007/s11786-011-0102-5
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DOI: https://doi.org/10.1007/s11786-011-0102-5