Kubična Hermiteova interpolacija z majhno oscilacijo odvodov

delo diplomskega seminarja

Nika Robida (Author), Emil Žagar (Mentor)

Abstract

V delu obravnavamo konstrukcijo interpolacijskih polinomov in polinomskih zlepkov. Definiramo strogo diagonalno dominatnost in indeks diagonalne dominatnosti matrike. Na podlagi izbranih točk in vrednosti zaporednih višjih odvodov zapišemo splošno Hermiteovo interpolacijsko formulo. Uporabo si ogledamo na primeru, ko so znane vrednosti prvih odvodov. Opišemo postopek iskanja kubičnih Hermiteovih interpolacijskih zlepkov, ki kar najmanj oscilirajo. Pri tem se poslužujemo optimizacije različnih funkcionalov z metodo najmanjših kvadratov. Analiziramo napako interpolacije. Opišemo interpolacijo parametričnih krivulj in vpliv izbire parametrizacije na obliko krivulje. Rezultati so prikazani na več numeričnih primerih.

Keywords

matematika;Hermiteova interpolacijska formula;kubična Hermiteova interpolacija;optimizacija odvodov;zlepki;stroga diagonalna dominantnost;

Data

Language:	Slovenian
Year of publishing:	2022
Typology:	2.11 - Undergraduate Thesis
Organization:	UL FMF - Faculty of Mathematics and Physics
Publisher:	[N. Robida]
UDC:	519.6
COBISS:	114910979
Views:	505
Downloads:	45
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	Cubic Hermite interpolation with small derivative oscillation
Secondary abstract:	The present diploma work deals with the construction of interpolation polynomials and polynomial splines. Strictly diagonal dominance and index of diagonally dominant matrix are defined. Based on given data points and values of consecutive higher order derivatives, formula for general Hermite interpolation is presented. We use that formula on the given data points with specified first derivatives at the interpolation points. The method for obtaining cubic Hermite interpolating spline with minimal derivative oscillation is described. In order to determine those polynomials, we consider functionals and the least squares method. We present the error analysis of the interpolant. Parametric curve design and the effect of the choice of interpolation parameters on visual appearance of the curve are described. The results are illustrated with several numerical examples.
Secondary keywords:	mathematics;Hermite interpolation formula;cubic Hermite interpolation;derivative optimization;splines;strictly diagonal dominance;
Type (COBISS):	Final seminar paper
Study programme:	0
Embargo end date (OpenAIRE):	1970-01-01
Thesis comment:	Univ. v Ljubljani, Fak. za matematiko in fiziko, Oddelek za matematiko, Matematika - 1. stopnja
Pages:	27 str.
ID:	15849439