20.500.12556/RUL-137977 Kubična Hermiteova interpolacija z majhno oscilacijo odvodov delo diplomskega seminarja Cubic Hermite interpolation with small derivative oscillation 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. 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. Hermiteova interpolacijska formula kubična Hermiteova interpolacija optimizacija odvodov zlepek stroga diagonalna dominantnost Hermite interpolation formula cubic Hermite interpolation derivative optimization spline strictly diagonal dominance true false false Slovenski jezik Angleški jezik Delo diplomskega seminarja/zaključno seminarsko delo/naloga 2022-07-07 08:15:02 2022-07-07 08:15:06 2024-05-29 12:22:52 0000-00-00 00:00:00 2022 0 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 519.6 123135 114910979 4429.pdf 4429.pdf 1 94119F339DCA6D115841B63DD63B31E9 15ac4119e08521cacfd6c8088b6e06bedcd8dbd10e60f1e7073f13e44009b166 ed2bb204-fdbb-11ec-8aca-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=158110 Fakulteta za matematiko in fiziko 0 0 0