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 37 of 58 Go Back Full Screen Close Quit Se aplică extrapolarea Richardson ¸si acestor valori. În general dacă f ∈ C2n+2 [a, b], atunci pentru k = 1, n putem scrie ⎡ ⎤ b a f(x)dx = hk 2 + k i=1 unde Ki nu depinde de hk. ⎣f(a) + f(b) + 2 Kih 2i k + O(h2k+2 k ), 2k−1 −1 i=1 f(a + ihk) ⎦ (29)
Introducere Derivare numerică Integrare numerică Cuadraturi adaptive Cuadraturi . . . Cuadraturi . . . Formule . . . Home Page Title Page ◭◭ ◮◮ ◭ ◮ Page 37 of 58 Go Back Full Screen Close Quit Se aplică extrapolarea Richardson ¸si acestor valori. În general dacă f ∈ C2n+2 [a, b], atunci pentru k = 1, n putem scrie ⎡ ⎤ b a f(x)dx = hk 2 + k i=1 ⎣f(a) + f(b) + 2 Kih 2i k + O(h2k+2 k ), 2k−1 −1 i=1 f(a + ihk) ⎦ unde Ki nu depinde de hk. Formula (29) se justifică în modul următor. Fie (29)
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Aproximarea functionalelor liniare

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