Aproximarea functionalelor liniare

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$P 0.1 Stabilişti natura şsi suma seriilor: a) Σ 1 n\ ; b) Σ arctan 1 n# + n ...$

Introducere Derivare numerică Integrare numerică Cuadraturi adaptive Cuadraturi . . . Cuadraturi . . . Formule . . . Home Page Title Page ◭◭ ◮◮ ◭ ◮ Page 48 of 58 Go Back Full Screen Close Quit Condit¸ia din (b) impune k condit¸ii asupra nodurilor t1, t2, . . . , tn din (32). (Dacă k = 0, nu avem nici o restrict¸ie, deoarece a¸sa cum ¸stim putem atinge gradul de exactitate d = n − 1).
Introducere Derivare numerică Integrare numerică Cuadraturi adaptive Cuadraturi . . . Cuadraturi . . . Formule . . . Home Page Title Page ◭◭ ◮◮ ◭ ◮ Page 48 of 58 Go Back Full Screen Close Quit Condit¸ia din (b) impune k condit¸ii asupra nodurilor t1, t2, . . . , tn din (32). (Dacă k = 0, nu avem nici o restrict¸ie, deoarece a¸sa cum ¸stim putem atinge gradul de exactitate d = n − 1). Într-adevăr un trebuie să fie ortogonale pe Pk−1 relativ la funct¸ia pondere w. Deoarece w(t) ≥ 0, avem în mod necesar k ≤ n. Altfel, un trebuie să fie ortogonal pe Pn, în particular pe el însu¸si, ceea ce este imposibil.
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Aproximarea functionalelor liniare

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