Creating and handling box valued functions used in numerical methods (Q1860414)

Let \(f: \mathbb{R}^n\to\mathbb{R}\) be continuous. A zone function \(Z_f\) of \(f\) is a function which assigns to each argument \(x\) of \(f\) and each value \(\alpha\in \mathbb{R}\), \(\alpha\neq f(x)\), an open neighbourhood, \(Z_f(x,\alpha)\), so that \(f(y)\neq\alpha\) for all \(y\in Z_f(x,\alpha)\). Zone functions can be applied as exclusion functions at searching for zeros or minimizers of \(f\). The paper is concerned with constructing zone functions recursively where the basic steps are the treatment of primitive functions like the arithmetic operations and the elementary transcendental functions. An implementation in \(C^{++}\) is given as well.