Funções de base radial de suporte global e compacto na aproximação de superfícies

Abstract

This study focuses onnumerical approximations throughtothe use of radial basis functions with compactly support (CSRBFs).These functions have been increasingly applied in multivariate approximation, being of great importance to several areas of science and engineering, such as meteorology, topography, seismology, among others. In these areas, usually applies the construction of a mapping surface from sparse experimental data, in which certain properties are collected to practical purposes.However, in these problems the number of parameters can range in the proportion of millions; because of this, computationally more economical procedures that reduce the risk of ill-conditioning of the problemand preserve their accuracy must be implemented. For this objective, one of the actions developed in this field is the use of CSRBFs. Thus,grounded in the approximation theory, this study aims to identify and analyze the regions of the domain of a test function, where the interpolation function or curve fitting function, hypothetically, would present difficulties of representing part of a surface with certain characteristic.Since, finding thisregionwould bepossibleto electacriterionforthereductionof centersofaradial basis functionfromthemethod ofleast squares.Finally, this study focuses on the comparative analysis and interpretation of the behavior of this class of functions in satisfactory representation of two-dimensional fields, regardingthe accuracy and computational cost. The results showed good performance in relation to the accuracy, both in curve fitting as in interpolation. One can notice that the use of a grid with equally spaced points is the most appropriate option fora more accurate approximation