@inproceedings{dur-far-kon-tah-14-aa-funcia,
  author = {Duracz, Jan and Farjudian, Amin and Kone{\v{c}}n{\'y}, Michal and Taha, Walid},
  title = {Function Interval Arithmetic},
  booktitle = {Proceedings of the4th International Conference on  Mathematical Software (ICMS)},
  location = {Seoul, KR},
  isbn = {978-3-662-44199-2},
  series = {Lecture Notes in Computer Science},
  volume = {8592},
  pages = {677–684},
  year = 2014,
  month = aug,
  doi = {10.1007/978-3-662-44199-2_101},
  comment = {Generalization of IA where the bounds can be arbitrary functions, e.g. polynomials. Claims that it is a generalization of AA, and is more precise.  But does not seem to record correlation between variables, and may have problems with multiplication when the functions cross zero. Or with non-linear operations in general, e. g. $\max$ or $\sqrt{}$.},
  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.}
}