Cell reducing and the dimension of the ▫$C^1$▫ bivariate spline space
Jaklič, Gašper
V ▫članku obravnavamo problem določitve dimenzije prostora $S_n^1 (\triangle), n \geq 3$▫ bivariatnih ▫$C^1$▫ zlepkov stopnje ▫$\leq n$▫ nad triangulacijo ▫$\triangle$▫. Funkcije, ki so odsekoma ...polinomi, predstavimo s šopki, pogoje gladkosti pa zapišemo kot sistem linearnih enačb. Rang sistemske matrike analiziramo s pomočjo ponavljajočih se reducirajočih majhnih podtrianguacij (celic) na robu triangulacije. Pokažemo, da je za velik razred triangulacij dimenzija bivariatnega prostora zlepkov ▫$S_n^1 (\triangle), n \geq 3$▫ enaka Schumakerjevi spodnji meji.
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