Solución numérica para el problema de Weber sobre una superficie regular usando geodésicas
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Date
2023
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Universidad Nacional de Trujillo
Abstract
El problema de Weber es un problema de la teoría de localización; el cual ha sido ampliamente tratado en la literatura, tanto teórica como empíricamente, gracias a su gran adaptabilidad a la modelación de situaciones reales. En el presente trabajo se ha estudiado el problema de Weber planteado sobre una superficie regular arbitraria; para lo cual se utilizan los modelos sobre el plano y la esfera de este problema, como base; identificándose aquellas propiedades y características a ser generalizadas. A partir de esto, se propone un algoritmo basado en la solución numérica de problemas de valor inicial asociado a geodésicas; lo cual permite aproximar las distancias en una superficie regular arbitraria, y, por tanto, aproximar la solución del problema de Weber sobre superficies regulares
ABSTRACT The Weber problem is a problem in localization theory; which has been largely treated in literature, so much theoretician like empirically, thanks to his great adaptability to the modelation of real situations. The Weber’s problem raised on a smooth surfaces is studied in the present work; by using the models on the plane and the sphere of this problem as base; identifying the properties and characteristic to be generalized. From this, we propose an algorithm based in the numerical solution of initial value problem associated with geodesics; which allow approximate distances in an arbitrary smooth surface, and therefore approximate the solution of Weber’s problem on smooth surfaces
ABSTRACT The Weber problem is a problem in localization theory; which has been largely treated in literature, so much theoretician like empirically, thanks to his great adaptability to the modelation of real situations. The Weber’s problem raised on a smooth surfaces is studied in the present work; by using the models on the plane and the sphere of this problem as base; identifying the properties and characteristic to be generalized. From this, we propose an algorithm based in the numerical solution of initial value problem associated with geodesics; which allow approximate distances in an arbitrary smooth surface, and therefore approximate the solution of Weber’s problem on smooth surfaces
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Keywords
Problema de Weber, Geodésicas