Schnurr, Marco The automatic computation of second-order slope tuples for some nonsmooth functions. (English) Zbl 1171.65013 ETNA, Electron. Trans. Numer. Anal. 30, 203-223 (2008). Summary: We show how the automatic computation of second-order slope tuples can be performed. The algorithm allows for nonsmooth functions, such as \(\varphi(x) = |u(x)|\) \(\varphi(x) = \max \{u(x),v(x)\}\), to occur in the function expression of the underlying function. Furthermore, we allow the function expression to contain functions given by two or more branches. By using interval arithmetic, second-order slope tuples provide verified enclosures of the range of the underlying function. We give some examples comparing range enclosures given by a second-order slope tuple with enclosures from previous papers. Cited in 2 Documents MSC: 65D25 Numerical differentiation 65G40 General methods in interval analysis Keywords:slope tuple; interval analysis; automatic slope computation; range enclosure; numerical examples; algorithm; nonsmooth functions Software:INTOPT_90 PDFBibTeX XMLCite \textit{M. Schnurr}, ETNA, Electron. Trans. Numer. Anal. 30, 203--223 (2008; Zbl 1171.65013) Full Text: EuDML EMIS