Generalized Convexity Properties and Shape-Based Approximation in Networks Reliability

Cristescu, Gabriela; Drăgoi, Vlad-Florin; Hoară, Sorin Horaţiu

doi:10.3390/math9243182

Open AccessArticle

Generalized Convexity Properties and Shape-Based Approximation in Networks Reliability

by

Gabriela Cristescu

^1,†

,

Vlad-Florin Drăgoi

^1,2,*,†

and

Sorin Horaţiu Hoară

^1,3,†

¹

Faculty of Exact Sciences, Aurel Vlaicu University of Arad, Bd. Revoluţiei, no. 77, 310130 Arad, Romania

²

LITIS, Rouen Normandie University, Avenue de l’Université, 76800 Saint-Étienne-du-Rouvray, France

³

Department of Computers and Information Technology, Polytechnic University of Timişoara, Piaţa Victoriei No. 2, 300006 Timişoara, Romania

^*

Author to whom correspondence should be addressed.

^†

These authors contributed equally to this work.

Mathematics 2021, 9(24), 3182; https://doi.org/10.3390/math9243182

Submission received: 17 November 2021 / Revised: 7 December 2021 / Accepted: 8 December 2021 / Published: 9 December 2021

(This article belongs to the Section E: Applied Mathematics)

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Abstract

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.

Keywords: network reliability; convex functions; quadratic spline functions; approximation

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MDPI and ACS Style

Cristescu, G.; Drăgoi, V.-F.; Hoară, S.H. Generalized Convexity Properties and Shape-Based Approximation in Networks Reliability. Mathematics 2021, 9, 3182. https://doi.org/10.3390/math9243182

AMA Style

Cristescu G, Drăgoi V-F, Hoară SH. Generalized Convexity Properties and Shape-Based Approximation in Networks Reliability. Mathematics. 2021; 9(24):3182. https://doi.org/10.3390/math9243182

Chicago/Turabian Style

Cristescu, Gabriela, Vlad-Florin Drăgoi, and Sorin Horaţiu Hoară. 2021. "Generalized Convexity Properties and Shape-Based Approximation in Networks Reliability" Mathematics 9, no. 24: 3182. https://doi.org/10.3390/math9243182

APA Style

Cristescu, G., Drăgoi, V.-F., & Hoară, S. H. (2021). Generalized Convexity Properties and Shape-Based Approximation in Networks Reliability. Mathematics, 9(24), 3182. https://doi.org/10.3390/math9243182

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Generalized Convexity Properties and Shape-Based Approximation in Networks Reliability

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