3 research outputs found
Optimal variable shape parameters using genetic algorithm for radial basis function approximation
Many radial basis function (RBF) methods contain free shape parameter or parameters that play an important role for the accuracy of the method. In most papers the authors end up choosing free shape parameter by trial and error or some other ad-hoc means. However, using variable shape parameters provides a clear potential for improved accuracy and stability of the RBF method. Already some progress has been reported to select usable variable shape parameters. In this paper, we propose applying the genetic algorithm to determine good variable shape parameters of radial basis functions for the solution of ordinary differential equations. Numerical results show that the proposed algorithm based on the genetic optimization is effective and provides reasonable shape parameters along with acceptable accuracy in linear and nonlinear case compared with other strategies to determine variable shape parameters
Nová strategie pro aproximaci rozptĂ˝lenĂ˝ch dat s vyuĹľitĂm radiálnĂch bázovĂ˝ch funkcĂ respektujĂcĂ body inflexe
Aproximace rozptĂ˝lenĂ˝ch dat je známá technika v poÄŤĂtaÄŤovĂ© vÄ›dÄ›. Navrhujeme novou strategii pro umĂstÄ›nĂ radiálnĂch základnĂch funkcĂ s ohledem na inflexnĂ body. UmĂstÄ›nĂ radiálnĂ základnĂ funkce má velkĂ˝ vliv na kvalitu aproximace. Z tohoto dĹŻvodu navrhujeme novou strategii pro umĂstÄ›nĂ radiálnĂch základnĂch funkcĂ s ohledem na vlastnosti aproximovanĂ© funkce, vÄŤetnÄ› extrĂ©mnĂch a inflexnĂch bodĹŻ. Naše experimentálnĂ vĂ˝sledky prokázaly vysokou kvalitu navrhovanĂ©ho pĹ™Ăstupu a vysokou kvalitu koneÄŤnĂ© aproximace.The approximation of scattered data is known technique in computer science. We propose a new strategy for the placement of radial basis functions respecting points of inflection. The placement of radial basis functions has a great impact on the approximation quality. Due to this fact we propose a new strategy for the placement of radial basis functions with respect to the properties of approximated function, including the extreme and the inflection points. Our experimental results proved high quality of the proposed approach and high quality of the final approximation
AnalĂ˝za podmĂnÄ›nosti radiálnĂch bázovĂ˝ch funkcĂ
GlobálnĂ radiálnĂ bázovĂ© funkce obecnÄ› vedou ke špatnÄ› podmĂnÄ›nĂ© soustavÄ› lineárnĂch rovnic. Tento pĹ™ĂspÄ›vek analyzuje podmĂnÄ›nost Gaussovy a „Thin Plate Spline“ (TPS) funkcĂ. Experimenty ukázaly závislost na tvarovĂ©m parametru a poÄŤtu bodĹŻ. Tato závislost lze popsat analyticky.The global RBFs lead to an ill-conditioned system of linear equations, in general. This contribution analyzes conditionality of the Gauss and the Thin Plate Spline (TPS) functions. Experiments made proved dependency of the shape parameter and number of points, which can be described as an analytical function