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filib++ is an extension of the interval library filib originally developed at the University of Karlsruhe. The most important aim of filib is the fast computation of guaranteed bounds for interval versions of a comprehensive set of elementary functions. filib++ extends this library in two aspects. First, it adds a second mode, the extended mode, that extends the exception-free computation mode (using special values to represent infinities and NaNs known from the IEEE floating-point standard 754) to intervals. In this mode, the so-called containment sets are computed to enclose the topological closure of a range of a function over an interval. Second, our new design uses templates and traits classes to obtain an efficient, easily extendable, and portable C++ library.

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We characterize the boundary ∂Σ p of the solution set Σ p of a parametric linear system A(p)x = b(p) where the elements of the n×n matrix and the right-hand side vector depend on a number of parameters p varying within interval bounds. The characterization of ∂Σ p is by means of pieces of parametric hypersurfaces, the latter represented by their coordinate functions depending on corresponding subsets of n − 1 parameters. The presented approach has a direct application for efficient visualization of parametric solution sets by utilizing some plotting functions supported by Mathematica and Maple. (2000): 15A06, 65G99, 65S05, 68U05. AMS subject classification