Generalized Convexity Properties and Shape-Based Approximation in Networks Reliability
Some properties of generalized convexity for sets and functions are identified in case of the reliability polynomials of two dual minimal networks. A method of approximating the reliability polynomials of two dual minimal network is developed based on their mutual complementarity properties. The app...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-12-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/24/3182 |
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| author | Gabriela Cristescu Vlad-Florin Drăgoi Sorin Horaţiu Hoară |
| author_facet | Gabriela Cristescu Vlad-Florin Drăgoi Sorin Horaţiu Hoară |
| author_sort | Gabriela Cristescu |
| collection | DOAJ |
| description | Some properties of generalized convexity for sets and functions are identified in case of the reliability polynomials of two dual minimal networks. A method of approximating the reliability polynomials of two dual minimal network is developed based on their mutual complementarity properties. The approximating objects are from the class of quadratic spline functions, constructed based on both interpolation conditions and shape knowledge. It is proved that the approximant objects preserve both the high-order convexity and some extremum properties of the exact reliability polynomials. It leads to pointing out the area of the network where the maximum number of paths is achieved. Numerical examples and simulations show the performance of the algorithm, both in terms of low complexity, small error and shape preserving. Possibilities of increasing the accuracy of approximation are discussed. |
| first_indexed | 2024-03-10T03:38:04Z |
| format | Article |
| id | doaj.art-5d0ccc01310c4a248ba666aaa306f60a |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T03:38:04Z |
| publishDate | 2021-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-5d0ccc01310c4a248ba666aaa306f60a2023-11-23T09:25:21ZengMDPI AGMathematics2227-73902021-12-01924318210.3390/math9243182Generalized Convexity Properties and Shape-Based Approximation in Networks ReliabilityGabriela Cristescu0Vlad-Florin Drăgoi1Sorin Horaţiu Hoară2Faculty of Exact Sciences, Aurel Vlaicu University of Arad, Bd. Revoluţiei, no. 77, 310130 Arad, RomaniaFaculty of Exact Sciences, Aurel Vlaicu University of Arad, Bd. Revoluţiei, no. 77, 310130 Arad, RomaniaFaculty of Exact Sciences, Aurel Vlaicu University of Arad, Bd. Revoluţiei, no. 77, 310130 Arad, RomaniaSome properties of generalized convexity for sets and functions are identified in case of the reliability polynomials of two dual minimal networks. A method of approximating the reliability polynomials of two dual minimal network is developed based on their mutual complementarity properties. The approximating objects are from the class of quadratic spline functions, constructed based on both interpolation conditions and shape knowledge. It is proved that the approximant objects preserve both the high-order convexity and some extremum properties of the exact reliability polynomials. It leads to pointing out the area of the network where the maximum number of paths is achieved. Numerical examples and simulations show the performance of the algorithm, both in terms of low complexity, small error and shape preserving. Possibilities of increasing the accuracy of approximation are discussed.https://www.mdpi.com/2227-7390/9/24/3182network reliabilityconvex functionsquadratic spline functionsapproximation |
| spellingShingle | Gabriela Cristescu Vlad-Florin Drăgoi Sorin Horaţiu Hoară Generalized Convexity Properties and Shape-Based Approximation in Networks Reliability Mathematics network reliability convex functions quadratic spline functions approximation |
| title | Generalized Convexity Properties and Shape-Based Approximation in Networks Reliability |
| title_full | Generalized Convexity Properties and Shape-Based Approximation in Networks Reliability |
| title_fullStr | Generalized Convexity Properties and Shape-Based Approximation in Networks Reliability |
| title_full_unstemmed | Generalized Convexity Properties and Shape-Based Approximation in Networks Reliability |
| title_short | Generalized Convexity Properties and Shape-Based Approximation in Networks Reliability |
| title_sort | generalized convexity properties and shape based approximation in networks reliability |
| topic | network reliability convex functions quadratic spline functions approximation |
| url | https://www.mdpi.com/2227-7390/9/24/3182 |
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