20.500.12556/RUL-171999 Iterativna aproksimacija s krivuljami delo diplomskega seminarja Iterative curve approximation Diplomska naloga obravnava geometrične iterativne metode za aproksimacijo podatkov s pomočjo krivulj, s poudarkom na B-zlepkih. Po uvodni predstavitvi Bézierjevih krivulj in de Casteljaujevega algoritma definiramo B-zlepke in progresivno iterativno aproksimacijo (PIA) ter njene različice, kot so WPIA, Jacobi–PIA, GS–PIA in SOR–PIA. Metode predstavimo tudi v matrični obliki. Za povečanje hitrosti konvergence uvedemo ustrezen predpogoj in analiziramo njegov vpliv na učinkovitost metod. Osnovne in predpogojevane metode uporabimo na primerih in jih med seboj primerjamo. The thesis discusses geometric iterative methods for data approximation using curves, with an emphasis on B-splines. After an introductory presentation of Bézier curves and the de Casteljau algorithm, we define B-splines and the progressive iterative approximation (PIA) method, along with its variants such as WPIA, Jacobi–PIA, GS–PIA, and SOR–PIA. The methods are also presented in their matrix form. To improve the convergence rate, we introduce an appropriate preconditioner and analyze its impact on the efficiency of the methods. Both the basic and preconditioned methods are applied to examples and compared. B-zlepki progresivna iterativna aproksimacija predpogojene iterativne metode B-splines progressive iterative approximation preconditioned iterative methods true false false Slovenski jezik Angleški jezik Delo diplomskega seminarja/zaključno seminarsko delo/naloga 2025-09-05 08:15:25 2025-09-05 08:15:26 2025-09-30 03:44:26 0000-00-00 00:00:00 2025 0 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 519.6 152604 247884035 18962.pdf 18962.pdf 1 35A67DC642AF77ACC4E35F2D1F12A84C a7cf805c74a6ad659212510799bc33541713eaf5b756449cf0ddaf65428503ef 903529ff-8a1f-11f0-9328-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=215717 Fakulteta za matematiko in fiziko 0 0 0