A Realistic Tolerant Solution of a System of Interval Linear Equations with the Use of Multidimensional Interval Arithmetic
The paper presents a method of determining the robustness of solutions of systems of interval linear equations (ILEs). The method can be applied also for the ILE systems for which it has been impossible to find solutions so far or for which solutions in the form of improper intervals have been obtai...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Sciendo
2023-06-01
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| Series: | International Journal of Applied Mathematics and Computer Science |
| Subjects: | |
| Online Access: | https://doi.org/10.34768/amcs-2023-0018 |
| _version_ | 1827916240471982080 |
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| author | Piegat Andrzej Pluciński Marcin |
| author_facet | Piegat Andrzej Pluciński Marcin |
| author_sort | Piegat Andrzej |
| collection | DOAJ |
| description | The paper presents a method of determining the robustness of solutions of systems of interval linear equations (ILEs). The method can be applied also for the ILE systems for which it has been impossible to find solutions so far or for which solutions in the form of improper intervals have been obtained (which cannot be implemented in practice). The research conducted by the authors has shown that for many problems it is impossible to arrive at ideal solutions that would be fully robust to data uncertainty. However, partially robust solutions can be obtained, and those with the highest robustness can be selected and put into practice. The paper shows that the degree of robustness to the uncertainty of the entire system can be calculated on the basis of the degrees of robustness of individual equations, which greatly simplifies calculations. The presented method is illustrated with a series of examples (also benchmark ones) that facilitate its understanding. It is an extension of the authors’ previously published method for first-order ILEs. |
| first_indexed | 2024-03-13T03:11:14Z |
| format | Article |
| id | doaj.art-c1e77bc2658b4b998b5850e4685d181b |
| institution | Directory Open Access Journal |
| issn | 2083-8492 |
| language | English |
| last_indexed | 2024-03-13T03:11:14Z |
| publishDate | 2023-06-01 |
| publisher | Sciendo |
| record_format | Article |
| series | International Journal of Applied Mathematics and Computer Science |
| spelling | doaj.art-c1e77bc2658b4b998b5850e4685d181b2023-06-26T10:48:37ZengSciendoInternational Journal of Applied Mathematics and Computer Science2083-84922023-06-0133222924710.34768/amcs-2023-0018A Realistic Tolerant Solution of a System of Interval Linear Equations with the Use of Multidimensional Interval ArithmeticPiegat Andrzej0Pluciński Marcin11Faculty of Computer Science and Information Systems, West Pomeranian University of TechnologyŻołnierska 49, 71-210Szczecin, Poland1Faculty of Computer Science and Information Systems, West Pomeranian University of TechnologyŻołnierska 49, 71-210Szczecin, PolandThe paper presents a method of determining the robustness of solutions of systems of interval linear equations (ILEs). The method can be applied also for the ILE systems for which it has been impossible to find solutions so far or for which solutions in the form of improper intervals have been obtained (which cannot be implemented in practice). The research conducted by the authors has shown that for many problems it is impossible to arrive at ideal solutions that would be fully robust to data uncertainty. However, partially robust solutions can be obtained, and those with the highest robustness can be selected and put into practice. The paper shows that the degree of robustness to the uncertainty of the entire system can be calculated on the basis of the degrees of robustness of individual equations, which greatly simplifies calculations. The presented method is illustrated with a series of examples (also benchmark ones) that facilitate its understanding. It is an extension of the authors’ previously published method for first-order ILEs.https://doi.org/10.34768/amcs-2023-0018interval arithmeticinterval linear equation systemtolerable solutionmultidimensional interval arithmetic |
| spellingShingle | Piegat Andrzej Pluciński Marcin A Realistic Tolerant Solution of a System of Interval Linear Equations with the Use of Multidimensional Interval Arithmetic International Journal of Applied Mathematics and Computer Science interval arithmetic interval linear equation system tolerable solution multidimensional interval arithmetic |
| title | A Realistic Tolerant Solution of a System of Interval Linear Equations with the Use of Multidimensional Interval Arithmetic |
| title_full | A Realistic Tolerant Solution of a System of Interval Linear Equations with the Use of Multidimensional Interval Arithmetic |
| title_fullStr | A Realistic Tolerant Solution of a System of Interval Linear Equations with the Use of Multidimensional Interval Arithmetic |
| title_full_unstemmed | A Realistic Tolerant Solution of a System of Interval Linear Equations with the Use of Multidimensional Interval Arithmetic |
| title_short | A Realistic Tolerant Solution of a System of Interval Linear Equations with the Use of Multidimensional Interval Arithmetic |
| title_sort | realistic tolerant solution of a system of interval linear equations with the use of multidimensional interval arithmetic |
| topic | interval arithmetic interval linear equation system tolerable solution multidimensional interval arithmetic |
| url | https://doi.org/10.34768/amcs-2023-0018 |
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