Iskanje minimuma na ploskvi : magistrsko delo

Močnik, Sara (author), Žagar, Emil (mentor)

V magistrskem delu si ogledamo interpolacijo ekvidistantnih točk v eni dimenziji in točk na regularni mreži v dveh dimenzijah, s poudarkom na bikubični interpolaciji. Opišemo optimizacijske metode za določanje minimuma funkcije z različnimi hitrostmi konvergence. Interpolacijo in metode preizkusimo na analitičnih funkcijah ter na realnih geodetskih podatkih.

• Language: Slovenian
• Keywords: interpolacija, optimizacija, minimizacija, Newtonova metoda, kvazi-Newtonova metoda, gradientna metoda, relief
• Work type: Master's thesis/paper
• Typology: 2.09 - Master's Thesis
• Organization: FMF - Faculty of Mathematics and Physics; FRI - Faculty of Computer and Information Science
• Year: 2022
• PID: 20.500.12556/RUL-142913
• UDC: 519.6
• COBISS.SI-ID: 132302083
• Publication date in RUL: 02.12.2022

Secondary language

• Language: English
• Title: Finding minimum on surface

Abstract

In this Master's Thesis we study interpolation of equidistant points in one dimension and points on regular grid in two dimensions, with an emphasis on bicubic interpolation. In addition we examine optimization methods for minimization of function with different convergence rates. First we test the presented interpolation and minimization methods with analytical functions, and then we move on to real geodetic data.

• Keywords: interpolation, optimization, minimization, Newton's method, Quasi- Newton method, gradient method, relief map