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 20 of 58 Go Back Full Screen Close Quit Fie f : [a, b] → R integrabilă pe [a, b], Fk(f), k = 0, m informat¸ii despre f (de regulă funct¸ionale <strong>liniare</strong>) ¸si w : [a, b] → R+ o funct¸ie pondere integrabilă pe [a, b]. Definit¸ia 10 O formulă de forma unde b a w(x)f(x)dx = Q(f) + R(f), (17) Q(f) = m AjFj(f), j=0 se nume¸ste formulă de integrare numerică a funct¸iei f sau formulă de cuadratură. Parametrii Aj, j = 0, m se numesc coeficient¸ii formulei, iar R(f) termenul rest al ei. Q se nume¸ste funct¸ională de cuadratură. Definit¸ia 11 Numărul natural d = d(Q) cu proprietatea că ∀ f ∈ Pd, R(f) = 0 ¸si ∃ g ∈ Pd+1 astfel încât R(g) = 0 se nume¸ste grad de exactitate al formulei de cuadratură .
Introducere Derivare numerică Integrare numerică Cuadraturi adaptive Cuadraturi . . . Cuadraturi . . . Formule . . . Home Page Title Page ◭◭ ◮◮ ◭ ◮ Page 21 of 58 Go Back Full Screen Close Quit Deoarece R este liniar, rezultă că o formulă de cuadratură are gradul de exactitate d dacă ¸si numai dacă R(ej) = 0, j = 0, d ¸si R(ed+1) = 0.
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Aproximarea functionalelor liniare

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