polynomial function enclosures (PFEs) approximating exact real functions.
AERN-RnToRm provides datatypes and abstractions for approximating functions of type D -> R^m where D is a bounded interval in R^n with non-empty interior.
The main datatype are function enclosures whose boundaries are piece-wise polynomial with a bounded degree. (This degree can be set arbitrarily high or as low as 0.) This datatype is supported by safely rounding operations whose precision can be increased arbitrarily, so that they all converge to the exact operations. Field operations, integration, maximisation and some elementary operations (namely exp, sin, cos) are among those already implemented.
For an architectural overview, see module Data.Number.ER.RnToRm.
A mathematical description of the very basics as well as a brief comparison with Taylor Models is included in the paper http://www-users.aston.ac.uk/~konecnym/papers/cfv08.html.
Simple examples of usage can be found in folder examples and a test suite can be run via the module in the folder tests.