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 54 of 58 Go Back Full Screen Close Quit Atunci nodurile tk sunt valori proprii ale lui Jn Jnvk = tkvk, v T k vk = 1, k = 1, 2, . . . , n, (40) iar ponderile wk sunt exprimabile cu ajutorul componentelor vk, ale vectorilor proprii normalizat¸i corespunzători prin wk = β0v 2 k,1 , k = 1, 2, . . . , n (41) Astfel, pentru a obt¸ine o formulă de cuadratură gaussiană trebuie rezolvată o problemă de vectori ¸si valori proprii pentru o matrice tridiagonală simetrică. Pentru această problemă există metode foarte eficiente. (v) Markov a observat că formula de cuadratură a lui Gauss poate fi obt¸inută cu ajutorul formulei de interpolare a lui Hermite. f(x) = (H2n−1f)(x) + u 2 n (x)f[x, x1, x1, . . . , xn, xn],
Introducere Derivare numerică Integrare numerică Cuadraturi adaptive Cuadraturi . . . Cuadraturi . . . Formule . . . Home Page Title Page ◭◭ ◮◮ ◭ ◮ Page 54 of 58 Go Back Full Screen Close Quit Atunci nodurile tk sunt valori proprii ale lui Jn Jnvk = tkvk, v T k vk = 1, k = 1, 2, . . . , n, (40) iar ponderile wk sunt exprimabile cu ajutorul componentelor vk, ale vectorilor proprii normalizat¸i corespunzători prin wk = β0v 2 k,1 , k = 1, 2, . . . , n (41) Astfel, pentru a obt¸ine o formulă de cuadratură gaussiană trebuie rezolvată o problemă de vectori ¸si valori proprii pentru o matrice tridiagonală simetrică. Pentru această problemă există metode foarte eficiente. (v) Markov a observat că formula de cuadratură a lui Gauss poate fi obt¸inută cu ajutorul formulei de interpolare a lui Hermite. b a f(x) = (H2n−1f)(x) + u 2 n (x)f[x, x1, x1, . . . , xn, xn], w(x)f(x)dx
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Aproximarea functionalelor liniare

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