| Complex Interval Function arcsin(z) in C-XSC (2008) | |||||||||||||||||
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| Frithjof Blomquist, Werner Hofschuster, Walter Krämer In C-XSC the complex interval standard functions f: C → C are implemented in cimath.cpp. For a function f and a given rectangular complex interval Z some inclusion interval W is computed, so that f(z) ∈ W holds for all z ∈ Z. Thereby real interval expressions must be evaluated on the boundary of Z, and a naive interval arithmetic often leads to premature overflow or to overestimations, if for example such expressions are evaluated near their zeros. In a new version these disadvantages are avoided by using different interval expressions in different regions on the boundary of Z, and so the intervals W are now optimal inclusions of the range of f(z), for z ∈ Z. As an example the strategy is presented by the inverse sine, and numerical results demonstrate the achieved improvements. | |||||||||||||||||
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