Levenberg-Marquardtov algoritem Levenberg-Marquardt algorithm V diplomski nalogi sta predstavljena Gauss–Newtonov algoritem (GNA) in metoda gradientnega spusta, na katerih temelji Levenberg–Marquardtov algoritem (LMA). LMA je iterativna metoda za reševanje nelinearnih enačb po metodi najmanjših kvadratov. Ključnega pomena pri njenem delovanju sta faktor dušenja in matrika dušenja. Z ustreznim prilagajanjem faktorja dušenja LMA prehaja med metodo gradientnega spusta, ki pomaga preprečevati izhlapevanje parametrov in GNA, ki omogoča hitro konvergenco vzdolž ozke doline stroškovne funkcije. Predstavljen je tudi način reševanja nelinearnih enačb z uporabo QR razcepa. V programskem okolju MATLAB sta implementirani funkciji, ki temeljita na Gauss–Newtonovem in Levenberg–Marquardtovem algoritmu. Z njuno pomočjo rešimo sistem nelinearnih enačb in primerjamo rezultate. In this thesis, the Gauss–Newton algorithm (GNA) and the gradient descent method, on which the Levenberg–Marquardt algorithm (LMA) is based, are presented. The LMA is an iterative method for solving nonlinear equations using the method of least squares. The damping parameter and the damping matrix play a key role in its performance. By appropriately adjusting the damping parameter, the LMA switches between the gradient descent method, which helps prevent parameter evaporation and the GNA, which enables rapid convergence along a narrow valley of the cost function. A method for solving nonlinear equations using QR decomposition is also presented. In the MATLAB programming environment, functions based on the Gauss–Newton and Levenberg–Marquardt algorithms are implemented. These functions are used to solve a system of nonlinear equations, and the obtained results are compared. Levenberg-Marquardtov algoritem Gauss-Newtonov algoritem metoda gradientnega spusta faktor dušenja nelinearen sistem QR razcep Levenberg-Marquardt algorithm Gauss-Newton algorithm gradient descent method damping parameter nonlinear system QR decomposition true false false Slovenski jezik Angleški jezik Diplomsko delo/naloga 2026-09-17 08:15:31 2026-09-17 08:15:34 2026-09-17 08:15:34 0000-00-00 00:00:00 2026 0 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 1970-01-01 164328 24148.pdf 24148.pdf 1 26622b86-b25f-11f1-8bc5-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=247823 Fakulteta za matematiko in fiziko 0 0 0