Método de interpolaciones sucesivas de Chebyshev para la obtención del polinomio óptimo - caso continuo

Abstract

The aim of this work was to elaborate a referential document entitled Çhebyshev’s method of successive interpolations to obtain the optimal polynomial, continuous case". The research was carried out by means of a methodological procedure with a qualitative approach at descriptive level, under a documentary type design, supported by bibliographic sources specialized in the topic. Subsequently, the acquired knowledge was applied to describe it in a reference document, which is composed of different properties of the numerical method. The main result generated by this degree work is a reference document composed of four sections: the first chapter deals with some starting numerical methods; the second section refers to different characteristics of the Chebyshev polynomials; the third chapter describes the Chebyshev method; and, in the fourth chapter, the implementation of the method is presented, alluding to several application examples. It is concluded that the roots or nodes of the Chebyshev polynomials are used as the best nodes in the polynomial interpolation, so that the error value is minimized. For future research, it is recommended to deepen on different numerical methods and to make a comparison to verify the method that gives us the smallest error.