Uz B-splainiem balstītas augstākas kārtas F-transformācijas

6533b7d4fe1ef96bd1263745

RESEARCH PRODUCT

Uz B-splainiem balstītas augstākas kārtas F-transformācijas

Mārtiņš Kokainis

subject

nestrikts sadalījums F-transformācija nestrikta kopa Matemātika B-splaini

description

Tiešā F-transformācija ir lineārs attēlojums no universā X (šajā darbā - intervāls [a;b]) definētām nepārtrauktām funkcijām uz vektoru telpu, kur vektora vērtības apraksta funkciju atbilstoši universa X nestriktam sadalījumam. Inversā F-transformācija attēlo tiešās F-transformācijas rezultātā iegūto vektoru par funkciju, kas aproksimē oriģinālo funkciju. Šīs pieejas vispārinājums ir augstākas kārtas F-transformācijas, kad tiešās transformācijas rezultātā iegūst vektoru ar polinomiālām komponentēm. Tiešās un inversās transformācijas īpašības ir būtiski atkarīgas no izvēlētā universa nestriktā sadalījuma. Šajā darbā tiek aplūkotas transformāciju īpašības, kad nestrikto sadalījumu iegūst ar B-splainu palīdzību; tiek parādīts, ka aprakstītā sadalījuma izvēle ļauj būtiski paaugstināt aproksimācijas kvalitāti, aproksimējot funkciju ar tās inverso Fm-transformāciju.

year	journal	country	edition	language
2015-01-01

https://dspace.lu.lv/dspace/handle/7/29702

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