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 12 of 58 Go Back Full Screen Close Quit 1.2. Metoda coeficient¸ilor nedeterminat¸i Aici determinăm coeficient¸ii din (3) astfel încât egalitatea să aibă loc ∀ f ∈ Φ, care, conform liniarităt¸ii lui L ¸si Li este echivalentă cu egalitatea pentru f = ϕ1, f = ϕ2, . . . , f = ϕm, adică ⎛ ⎞ m ⎝ ⎠ ϕi = Lϕi, i = 1, m, sau conform (8) j=1 ajLj m ajLjϕi = λi, i = 1, m. j=1
Introducere Derivare numerică Integrare numerică Cuadraturi adaptive Cuadraturi . . . Cuadraturi . . . Formule . . . Home Page Title Page ◭◭ ◮◮ ◭ ◮ Page 12 of 58 Go Back Full Screen Close Quit 1.2. Metoda coeficient¸ilor nedeterminat¸i Aici determinăm coeficient¸ii din (3) astfel încât egalitatea să aibă loc ∀ f ∈ Φ, care, conform liniarităt¸ii lui L ¸si Li este echivalentă cu egalitatea pentru f = ϕ1, f = ϕ2, . . . , f = ϕm, adică ⎛ ⎞ m ⎝ ⎠ ϕi = Lϕi, i = 1, m, sau conform (8) j=1 ajLj m ajLjϕi = λi, i = 1, m. j=1 Evident, matricea sistemului este G T , deci în concordant¸ă cu (10). a = [a1, a2, . . . , am] T = (G T ) −1 λ,
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Aproximarea functionalelor liniare

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