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The automatic computation of second-order slope tuples for some nonsmooth functions. (English) Zbl 1171.65013

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.

MSC:

65D25 Numerical differentiation
65G40 General methods in interval analysis

Software:

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