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 55 of 58 Go Back Full Screen Close Quit b a deci Dar gradul de exactitate 2n − 1 implică b a w(x)(H2n−1f)(x)dx = w(x)f(x)dx = Rn(f) = n wif(xi) + i=1 n wi(H2n−1f)(xi) = i=1 b a n wif(xi), i=1 w(x)u 2 (x)f[x, x1, x1, . . . , xn, xn]dx, b w(x)u a 2 n (x)f[x, x1, x1, . . . , xn, xn]dx. Cum w(x)u 2 (x) ≥ 0, aplicând teorema de medie pentru integrale ¸si teorema de medie pentru diferent¸e divizate avem
Introducere Derivare numerică Integrare numerică Cuadraturi adaptive Cuadraturi . . . Cuadraturi . . . Formule . . . Home Page Title Page ◭◭ ◮◮ ◭ ◮ Page 55 of 58 Go Back Full Screen Close Quit b a deci Dar gradul de exactitate 2n − 1 implică b a w(x)(H2n−1f)(x)dx = w(x)f(x)dx = Rn(f) = n wif(xi) + i=1 n wi(H2n−1f)(xi) = i=1 b a n wif(xi), i=1 w(x)u 2 (x)f[x, x1, x1, . . . , xn, xn]dx, b w(x)u a 2 n (x)f[x, x1, x1, . . . , xn, xn]dx. Cum w(x)u 2 (x) ≥ 0, aplicând teorema de medie pentru integrale ¸si teorema de medie pentru diferent¸e divizate avem Rn(f)
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Aproximarea functionalelor liniare

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