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 44 of 58 Go Back Full Screen Close Quit 7. Formule Newton-Cotes cu ponderi ¸si formule de tip Gauss O formulă de cuadratură cu ponderi este o formulă de tipul b a f(t)w(t)dt = n wkf(tk) + Rn(f) (32) k=1 unde w este nenegativă, integrabilă pe (a, b). Intervalul (a, b) poate fi mărginit sau nemărginit. Dacă este nemărginit trebuie să ne asigurăm că integrala din (32) este bine definită, cel put¸in în cazul când f este polinom. Realizăm aceasta cerând ca toate momentele funct¸iei pondere b µs = a t s w(t)dt, s = 0, 1, 2, . . . (33)
Introducere Derivare numerică Integrare numerică Cuadraturi adaptive Cuadraturi . . . Cuadraturi . . . Formule . . . Home Page Title Page ◭◭ ◮◮ ◭ ◮ Page 44 of 58 Go Back Full Screen Close Quit 7. Formule Newton-Cotes cu ponderi ¸si formule de tip Gauss O formulă de cuadratură cu ponderi este o formulă de tipul b a f(t)w(t)dt = n wkf(tk) + Rn(f) (32) k=1 unde w este nenegativă, integrabilă pe (a, b). Intervalul (a, b) poate fi mărginit sau nemărginit. Dacă este nemărginit trebuie să ne asigurăm că integrala din (32) este bine definită, cel put¸in în cazul când f este polinom. Realizăm aceasta cerând ca toate momentele funct¸iei pondere b µs = a să existe ¸si să fie finite. t s w(t)dt, s = 0, 1, 2, . . . (33)
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Aproximarea functionalelor liniare

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