Problema inverso de Weber en la esfera unitaria
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Date
2024
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Universidad Nacional de Trujillo
Abstract
El problema inverso de Weber en el plano consiste en encontrar pesos asociados con n puntos fijos en el plano, asegurando que un punto dado a priori sea la mediana geométrica ponderada euclideana. La presente investigación aborda el problema inverso de Weber en la esfera unitaria generalizando el problema inverso de Weber en el plano. En esta investigación se utiliza un subespacio ortogonal a un subespacio generado por dos vectores a y b asociados con los puntos y pesos dados. Como principal aporte de este trabajo se tiene que una solución del problema inverso de Weber en la esfera unitaria está formada por las componentes de un vector de componentes positivas que es ortogonal a los vectores a y b, en Rn. Además, se desarrolla un algoritmo y su respectivo programa en los lenguajes de Octave y Python de esta solución. Se dan ejemplos de aplicación en la esfera unitaria
Abstract The inverse Weber problem in the plane consists of finding weights associated with n fixed points in the plane, ensuring that a point given a priori is the Euclidean weighted geometric median. This research addresses the problem Weber inverse on the unit sphere generalizing the Weber inverse problem on the plane. In this research, a subspace orthogonal to a subspace generated by two vectors a and b associated with the given points and weights is used. The main contribution of this work is that a solution to the inverse Weber problem in the unit sphere is formed by the components of a vector of positive components that is orthogonal to the vectors a and b, in Rn. In addition, an algorithm and its respective program are developed in the Octave and Python languages of this solution. Examples of application in the unit sphere are given
Abstract The inverse Weber problem in the plane consists of finding weights associated with n fixed points in the plane, ensuring that a point given a priori is the Euclidean weighted geometric median. This research addresses the problem Weber inverse on the unit sphere generalizing the Weber inverse problem on the plane. In this research, a subspace orthogonal to a subspace generated by two vectors a and b associated with the given points and weights is used. The main contribution of this work is that a solution to the inverse Weber problem in the unit sphere is formed by the components of a vector of positive components that is orthogonal to the vectors a and b, in Rn. In addition, an algorithm and its respective program are developed in the Octave and Python languages of this solution. Examples of application in the unit sphere are given
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Keywords
Función de Weber, esfera unitaria, vector ortogonal