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 2 of 58 Go Back Full Screen Close Quit 1. Introducere Fie X un spat¸iu liniar, L1, . . . , Lm funct¸ionale <strong>liniare</strong> reale, liniar independente, definite pe X ¸si L : X → R o funct¸ională liniară reală astfel încât L, L1, . . . , Lm să fie liniar independente. Definit¸ia 1 O formulă de aproximare a funct¸ionalei L în raport cu funct¸ionalele L1, . . . , Lm este o formulă de forma L(f) = m AiLi(f) + R(f), f ∈ X. (1) i=1 Parametrii reali Ai se numesc coeficient¸ii formulei, iar R(f) termenul rest. Pentru o formulă de aproximare de forma (1), dându-se funct¸ionalele Li, se pune problema determinării coeficient¸ilor Ai ¸si a studiului termenului rest corespunzător valorilor obt¸inute pentru coeficient¸i.
Introducere Derivare numerică Integrare numerică Cuadraturi adaptive Cuadraturi . . . Cuadraturi . . . Formule . . . Home Page Title Page ◭◭ ◮◮ ◭ ◮ Page 2 of 58 Go Back Full Screen Close Quit 1. Introducere Fie X un spat¸iu liniar, L1, . . . , Lm funct¸ionale <strong>liniare</strong> reale, liniar independente, definite pe X ¸si L : X → R o funct¸ională liniară reală astfel încât L, L1, . . . , Lm să fie liniar independente. Definit¸ia 1 O formulă de aproximare a funct¸ionalei L în raport cu funct¸ionalele L1, . . . , Lm este o formulă de forma L(f) = m AiLi(f) + R(f), f ∈ X. (1) i=1 Parametrii reali Ai se numesc coeficient¸ii formulei, iar R(f) termenul rest. Pentru o formulă de aproximare de forma (1), dându-se funct¸ionalele Li, se pune problema determinării coeficient¸ilor Ai ¸si a studiului termenului rest corespunzător valorilor obt¸inute pentru coeficient¸i. Observat¸ia 2 Forma funct¸ionalelor Li depinde de informat¸iile det¸inute asupra lui f (ele exprimând de fapt aceste informat¸ii), dar ¸si de natura problemei de aproximare, adică de forma lui L.
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Aproximarea functionalelor liniare

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