Birkhofa interpolācija

6533b853fe1ef96bd12ac622

RESEARCH PRODUCT

Birkhofa interpolācija

Mārtiņš Kokainis

subject

description

Birkhofa interpolācija ir Ermita interpolācijas vispārinājums: tajā tiek meklēta funkcija, kuras atvasinājumi interpolācijas mezglos pieņem noteiktas vērtības, turklāt var uzdot atvasinājumu vērtības, neuzdodot zemākas kārtas atvasinājumu vai pašas funkcijas vērtības. Atšķirībā no Ermita interpolācijas, Birkhofa interpolācijas problēmai ne vienmēr eksistē atrisinājums. Darbā aplūkota Birkhofa interpolācija vispārīgā gadījumā, interpolācija ar polinomiem un ar polinomiāliem splainiem. Interpolējot ar polinomiem, definēts regulārs režģis un raksturoti gadījumi, kad režģis ir regulārs. Tiek arī aprakstītas interpolācijas režģa afīnu transformāciju īpašības. Interpolējot ar splainiem, vispārināta teorēma par interpolējošā splaina eksistences nosacījumiem, aprakstīta situācija, kad interpolācijas nosacījumi ir uzdoti specifiskā veidā (pēc vienota šablona). Īpaša uzmanība veltīta variāciju pieejai Birkhofa interpolācijai.

year	journal	country	edition	language
2013-01-01

https://dspace.lu.lv/dspace/handle/7/21736

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