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 5 of 58 Go Back Full Screen Close Quit Observat¸ia 7 Deoarece R este o funct¸ională liniară proprietatea Ker(R) = Pr este echivalentă cu R(ek) = 0, k = 0, r ¸si R(er+1) = 0, unde ek(x) = x k . Putem acum să formulăm problema generală de aproximare: dându-se o funct¸ională liniară L pe X, m funct¸ionale <strong>liniare</strong> L1, L2, . . . , Lm pe X ¸si valorile lor (”datele”) ℓi = Lif, i = 1, m aplicate unei anumite funct¸ii f ¸si un subspat¸iu liniar Φ ⊂ X cu dim Φ = m, dorim să găsim o formulă de aproximare de tipul
Introducere Derivare numerică Integrare numerică Cuadraturi adaptive Cuadraturi . . . Cuadraturi . . . Formule . . . Home Page Title Page ◭◭ ◮◮ ◭ ◮ Page 5 of 58 Go Back Full Screen Close Quit Observat¸ia 7 Deoarece R este o funct¸ională liniară proprietatea Ker(R) = Pr este echivalentă cu R(ek) = 0, k = 0, r ¸si R(er+1) = 0, unde ek(x) = x k . Putem acum să formulăm problema generală de aproximare: dându-se o funct¸ională liniară L pe X, m funct¸ionale <strong>liniare</strong> L1, L2, . . . , Lm pe X ¸si valorile lor (”datele”) ℓi = Lif, i = 1, m aplicate unei anumite funct¸ii f ¸si un subspat¸iu liniar Φ ⊂ X cu dim Φ = m, dorim să găsim o formulă de aproximare de tipul Lf ≈ m aiLif (2) i=1
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Aproximarea functionalelor liniare

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