Precise optimization using range arithmetic

AbstractIn a recent paper by Aberth and Schaefer (1992), it was shown how an implementation of range arithmetic in the programming language C+ + can serve as a basis for writing numerical programs which compute reliable answers. This arithmetic is more complex than floating-point arithmetic and is a form of interval arithmetic. Here we show how a search algorithm for local minima of smooth unconstrained functions can be adapted to range arithmetic in order to guarantee convergence and generate correct results