An effective method for division of rectangular intervals

This paper focuses on the division of intervals in rectangular form. The particular case where the intervals are in the complex plane is considered. For two rectangular complex intervals [Z.sub.1] and [Z.sub.2] finding the smallest rectangle containing the exact set {[z.sub.1] * [z.sub.2] : [z.sub.1] [member of] [Z.sub.1], [z.sub.2] [member of] [Z.sub.2]} of the operation * [member of] {+, -, *, /} is the main objective of complex interval arithmetic. For the operations addition, subtraction and multiplication, the optimal solution can be easily found. In the case of division the solution requires rather complicated calculations. This is due to the fact that space of rectangular intervals is not closed under division. The quotient of two rectangular intervals is an irregular shape in general. This work introduces a new method for the determination of the smallest rectangle containing the result in the case of division. The method obtains the optimal solution with less computational cost compared to the algorithms currently available. Keywords: interval arithmetic; interval division; complex interval; rectangular interval; global optimization Mathematics Subject Classification: 65G30, 65G40, 65Y04