Evaluation algorithm for a decomposed simplicial piecewise-linear formulation

 

V.M. Jiménez-Fernández¹, J. Agustín-Rodríguez², P. Marcelo-Julián², O. Agamennoni²

 

¹ National Institute for Astrophysics, Optics and Electronics, Department of Electronics, Luis Enrique Erro No.1, Santa María Tonantzintla, P.O. 72840 Puebla, México.

² Universidad Nacional del Sur, Departamento de Ingeniería Eléctrica y de Computadoras, Av. Alem No. 1253, P.O. 8000 Bahía Blanca, Argentina.

 

ABSTRACT

In this work an algorithm for the evaluation of N-dimensional piecewise-linear (PWL) functions is presented. The type of PWL representation which is considered is the denominated simplicial representation that is defined in a N-dimensional domain partitioned by hyperplanes and divided into simplices. The algorithm performs a local function computation into the specific simplex where the evaluation point is found. The simplicial PWL (S-PWL) interpolating equations are collected into a matrix system which adopts the form of the decomposed PWL models. The algorithm works directly with this decomposed model and determines the value of the S-PWL function simply by its values on the vertices.

Keywords: Simplicial, Piecewise-Linear, Evaluation.

 

RESUMEN

En este trabajo se presenta un algoritmo para la evaluación de funciones lineales a tramos (LAT) N-dimensionales. El tipo de representación LAT que es considerado es el denominado descripción simplicial que se define en un dominio N-dimensional particionado por hiperplanos y dividido en símplices. El algoritmo realiza un cómputo local de la función en el símplice específico donde se encuentra el punto de evaluación. Las ecuaciones de interpolación de la representación LAT simplicial (LAT-S) son colectadas en un sistema matricial que adopta la forma de los modelos LAT descompuestos. El algoritmo trabaja directamente con este modelo descompuesto y determina el valor de la función LAT-S simplemente mediante su valor en los vértices. 

 

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