magistrsko delo
Maša Vinter (Author), Marjetka Krajnc (Mentor)

Abstract

V tem delu obravnavamo problem aproksimacije razpršenih podatkov v eni in več dimenzijah. Ker je znano, da pri aproksimaciji s polinomi z več spremenljivkami obstajajo omejitve glede izbire interpolacijskih točk, ki zagotavljajo obstoj in enoličnost interpolantov, tukaj predstavimo aproksimacijo z radialnimi baznimi funkcijami. Prednost radialnih baznih funkcij je, da so definirane z normo, zato se pri delu z njimi izognemu računanju v večih dimenzijah. Predstavljeni so pogoji, ki morajo za izbrane radialne bazne funkcije veljati, da bo rešitev interpolacijskega problema obstajala in bo enolična, ter primeri ustreznih družin funkcij. Omenjeni so tudi problemi, ki lahko nastanejo pri interpolaciji z radialnimi baznimi funkcijami. Opisan je način interpolacije s polinomsko natačnostjo in pogoji, ki morajo pri tem veljati. Na kratko je predstavljena tudi možnost uporabe radialnih baznih funkcij pri aproksimaciji z metodo najmanjših kvadratov in prednosti te metode.

Keywords

interpolacija;radialne bazne funkcije;aproksimacija po metodi najmanjših kvadratov;

Data

Language: Slovenian
Year of publishing:
Typology: 2.09 - Master's Thesis
Organization: UL FMF - Faculty of Mathematics and Physics
Publisher: [M. Vinter]
UDC: 519.6
COBISS: 18626393 Link will open in a new window
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Downloads: 210
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Other data

Secondary language: English
Secondary title: Scattered data approximation with radial basis functions
Secondary abstract: The topic of this thesis is approximation of scattered data in one and multiple dimensions. Given the fact that approximation with multivariate polynomials has some restrictions regarding the choice of interpolation points that guarantee the problem to be well-posed, we propose approximation with radial basis functions. Since radial basis functions are defined with a norm we can avoid dealing with calculations in multiple dimensions. We present the conditions that have to hold for radial basis functions so that solution exists and is unique. We also present a few examples of families of functions that fulfill these conditions and problems that can arise when interpolating with radial basis functions. The manner of interpolation with polynomial precision and the conditions that have to be met are described too. We briefly present the possibility of using radial basis functions in least squares approximation and the advantages of this method.
Secondary keywords: interpolation;radial basis functions;least squares approximation;
Type (COBISS): Master's thesis/paper
Study programme: 0
Thesis comment: Univ. v Ljubljani, Fak. za matematiko in fiziko, Oddelek za matematiko, Računalništvo in matematika - 2. stopnja
Pages: IX, 53 str.
ID: 11117193
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