20.500.12556/RUL-160936 Kvazi-interpolacija z B-zlepki Quasi-interpolation with B-splines V diplomskem delu se ukvarjamo s kvazi-interpolacijo. Pri klasični interpolaciji želimo potegniti krivuljo skozi vse podane točke, kar tipično privede do reševanja velikega sistema linearnih enačb, s kvazi-interpolacijo pa rešujemo več manjših, lokalnih sistemov. Pri kvazi-interpolaciji točk ne interpoliramo, temveč se jim dovolj dobro približamo. K nalogi pristopamo tako, da najprej pogledamo primer interpolacije s polinomi, potem pa definiramo in pojasnimo osnovne gradnike obravnavanih kvazi-interpolantov, to so t.i. B-zlepki. Zatem kvazi-interpolacijo formalno definiramo in dokažemo red konvergence za izbrane kvazi-interpolante. Tekom naloge izpeljane metode tudi implementiramo in jih prikažemo na grafih. Na koncu izpeljemo lokalno metodo najmanjših kvadratov in si pogledamo praktičen primer uporabe kvazi-interpolacije z odstranitvijo šuma iz signala. In this thesis, we focus on quasi-interpolation. In classical interpolation, the goal is to draw a curve through all given points, which often results in a large system of linear equations. Quasi-interpolation, on the other hand, involves solving several smaller, local systems. With quasi-interpolation, we do not interpolate the points directly; instead, we approximate them sufficiently well. Our approach begins by examining an example of interpolation with polynomials, followed by the definition and explanation of the fundamental building blocks of quasi-interpolants, namely B-splines. We then formally define quasi-interpolation and prove the order of convergence for chosen quasi-interpolants. Throughout the thesis, we implement the derived methods and present them graphically. Finally, we derive the local method of least squares and explore a practical application of quasi-interpolation in noise removal from a signal. B-zlepki aproksimacija interpolacija kvazi-interpolacija B-splines approximation interpolation quasi-interpolation true false false Slovenski jezik Angleški jezik Diplomsko delo/naloga 2024-09-05 15:35:00 2024-09-05 15:35:06 2024-10-03 11:11:54 0000-00-00 00:00:00 2024 0 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 37534 210057475 Korotaj_Luka_-_Kvazi-interpolacija_z_B-zlepki.pdf Korotaj_Luka_-_Kvazi-interpolacija_z_B-zlepki.pdf 1 AE944D6E5FEC01C4CDFF61554DCB24C9 dfcf6656441e88b9aa4ba660657c086b2742e4db5933a15384a70c137f92543a a8172e22-6b8b-11ef-b232-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=189769 Fakulteta za računalništvo in informatiko 0 0 0