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 53 of 58 Go Back Full Screen Close Quit Proprietatea care urmează este baza unui algoritm eficient de obt¸inere a unor formule de cuadratură gaussiană. (iv) Fie αk = αk(w) ¸si βk = βk(w) coeficient¸ii din formula de recurent¸ă pentru polinoamele ortogonale πk+1(t) = (t − αk)πk(t) − βkπk−1(t), k = 0, 1, 2, . . . (39) cu β0 definit (ca de obicei) prin π0(t) = 1, π−1(t) = 0, b β0 = a w(t)dt (= µ0). Matricea Jacobi de ordinul n pentru funct¸ia pondere w este o matrice simetrică tridiagonală definită prin ⎡ α0 √ ⎢ β1 ⎢ Jn(w) = ⎢ ⎣ √ β1 α1 √ β2 √ β2 . .. . .. . .. 0 √ 0 ⎤ ⎥ . ⎥ βn−1 ⎦ √ βn−1 αn−1
Introducere Derivare numerică Integrare numerică Cuadraturi adaptive Cuadraturi . . . Cuadraturi . . . Formule . . . Home Page Title Page ◭◭ ◮◮ ◭ ◮ Page 53 of 58 Go Back Full Screen Close Quit Proprietatea care urmează este baza unui algoritm eficient de obt¸inere a unor formule de cuadratură gaussiană. (iv) Fie αk = αk(w) ¸si βk = βk(w) coeficient¸ii din formula de recurent¸ă pentru polinoamele ortogonale πk+1(t) = (t − αk)πk(t) − βkπk−1(t), k = 0, 1, 2, . . . (39) cu β0 definit (ca de obicei) prin π0(t) = 1, π−1(t) = 0, b β0 = a w(t)dt (= µ0). Matricea Jacobi de ordinul n pentru funct¸ia pondere w este o matrice simetrică tridiagonală definită prin ⎡ α0 √ ⎢ β1 ⎢ Jn(w) = ⎢ ⎣ √ β1 α1 √ β2 √ β2 . .. . .. . .. 0 √ 0 ⎤ ⎥ . ⎥ βn−1 ⎦ √ βn−1 αn−1
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Introducere Derivare numerică Inte
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Aproximarea functionalelor liniare

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