### AIMS Mathematics

2020, Issue 6: 6355-6372. doi: 10.3934/math.2020409
Research article

# An effective method for division of rectangular intervals

• Received: 05 June 2020 Accepted: 30 July 2020 Published: 10 August 2020
• MSC : 65G30, 65G40, 65Y04

• 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 $Z_{1}$ and $Z_{2}$ finding the smallest rectangle containing the exact set $\left\{ z_{1}\ast z_{2}:z_{1}\in Z_{1}, z_{2}\in Z_{2}\right\}$ of the operation $\ast\in\{+, -, \cdot, \diagup\}$ 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.

Citation: Edrees M. Nori Mahmood, Gultekin Soylu. An effective method for division of rectangular intervals[J]. AIMS Mathematics, 2020, 5(6): 6355-6372. doi: 10.3934/math.2020409

### Related Papers:

• 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 $Z_{1}$ and $Z_{2}$ finding the smallest rectangle containing the exact set $\left\{ z_{1}\ast z_{2}:z_{1}\in Z_{1}, z_{2}\in Z_{2}\right\}$ of the operation $\ast\in\{+, -, \cdot, \diagup\}$ 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.

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沈阳化工大学材料科学与工程学院 沈阳 110142

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