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 47 of 58 Go Back Full Screen Close Quit Chestiunea care se pune în mod natural este dacă nu am putea face aceasta mai bine, adică dacă nu am putea obt¸ine gradul de exactitate d > n − 1 printr-o alegere judicioasă a nodurilor tk (ponderile wk fiind date în mod necesar de (35)). Răspunsul este surprinzător de simplu ¸si de direct. Pentru a-l formula, considerăm polinomul nodurilor un(t) = n (t − tk). (37) k=1 Teorema 12 Dându-se un întreg k, 0 ≤ k ≤ n, formula de cuadratură (32) are gradul de exactitate d = n − 1 + k dacă ¸si numai dacă sunt satisfăcute următoarele condit¸ii: (a) formula (32) este de tip interpolator; (b) polinomul nodurilor un din (37) satisface b a un(t)p(t)w(t) dt = 0, ∀ p ∈ Pk−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
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