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 42 of 58 Go Back Full Screen Close Quit Fie c = (a + b)/2. Formula elementară a lui Simpson este S = h (f(a) + 4f(c) + f(b)) . 6 Pentru două subintervale se obt¸ine S2 = h (f(a) + 4f(d) + 2f(c) + 4f(e) + f(b)) , 12 unde d = (a + c)/2 ¸si e = (c + b)/2. Cantitatea Q se obt¸ine aplicând (31) celor două aproximante: Q = S2 + (S2 − S)/15.
Introducere Derivare numerică Integrare numerică Cuadraturi adaptive Cuadraturi . . . Cuadraturi . . . Formule . . . Home Page Title Page ◭◭ ◮◮ ◭ ◮ Page 42 of 58 Go Back Full Screen Close Quit Fie c = (a + b)/2. Formula elementară a lui Simpson este S = h (f(a) + 4f(c) + f(b)) . 6 Pentru două subintervale se obt¸ine S2 = h (f(a) + 4f(d) + 2f(c) + 4f(e) + f(b)) , 12 unde d = (a + c)/2 ¸si e = (c + b)/2. Cantitatea Q se obt¸ine aplicând (31) celor două aproximante: Q = S2 + (S2 − S)/15. Putem să dam acum un algoritm recursiv pentru aproximarea integralei. Funct¸ia adquad evaluează integrandul aplicând regula lui Simson. Ea apelează recursiv quadstep ¸si aplică extrapolarea. Descrierea se dă în algoritmul 2.
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Aproximarea functionalelor liniare

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