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 $Z_{1}$ and $Z_{2}$ finding the smallest rectangle containing the exact set $\left\{ z_{1}\ast z_{2}:z_{1}\in Z_{...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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AIMS Press
2020-08-01
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| Series: | AIMS Mathematics |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/10.3934/math.2020409/fulltext.html |
| _version_ | 1818242738453217280 |
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| author | Edrees M. Nori Mahmood Gultekin Soylu |
| author_facet | Edrees M. Nori Mahmood Gultekin Soylu |
| author_sort | Edrees M. Nori Mahmood |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-12T13:50:00Z |
| format | Article |
| id | doaj.art-3d565778c90c4906bcc6796b1ddf42a3 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-12-12T13:50:00Z |
| publishDate | 2020-08-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-3d565778c90c4906bcc6796b1ddf42a32022-12-22T00:22:35ZengAIMS PressAIMS Mathematics2473-69882020-08-01566355637210.3934/math.2020409.An effective method for division of rectangular intervalsEdrees M. Nori Mahmood0Gultekin Soylu11 Department of Operations Research and Intelligent Techniques, University of Mosul, Iraq2 Department of Mathematics, Akdeniz University, Antalya, 07058, TurkeyThis 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.https://www.aimspress.com/article/10.3934/math.2020409/fulltext.htmlinterval arithmeticinterval divisioncomplex intervalrectangular intervalglobal optimization |
| spellingShingle | Edrees M. Nori Mahmood Gultekin Soylu An effective method for division of rectangular intervals AIMS Mathematics interval arithmetic interval division complex interval rectangular interval global optimization |
| title | An effective method for division of rectangular intervals |
| title_full | An effective method for division of rectangular intervals |
| title_fullStr | An effective method for division of rectangular intervals |
| title_full_unstemmed | An effective method for division of rectangular intervals |
| title_short | An effective method for division of rectangular intervals |
| title_sort | effective method for division of rectangular intervals |
| topic | interval arithmetic interval division complex interval rectangular interval global optimization |
| url | https://www.aimspress.com/article/10.3934/math.2020409/fulltext.html |
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