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 46 of 58 Go Back Full Screen Close Quit Observăm că dacă se dau n noduri distincte t1, . . . , tn este posibil întotdeauna să construim o formulă de tip (32) care este exactă pentru orice polinom de grad ≤ n − 1. În cazul w(t) ≡ 1 pe [−1, 1] ¸si tk sunt echidistante pe [−1, 1] problema a fost intuită de Newton în 1687 ¸si rezolvată în detaliu de Cotes în jurul anului 1712. Prin extensie vom numi formula (32) cu tk prescrise ¸si wk date de (35) formulă de tip Newton-Cotes .
Introducere Derivare numerică Integrare numerică Cuadraturi adaptive Cuadraturi . . . Cuadraturi . . . Formule . . . Home Page Title Page ◭◭ ◮◮ ◭ ◮ Page 47 of 58 Go Back Full Screen Close Quit (a) Sir Isaac Newton (1643 - 1727) Figura 7: (b) Roger Cotes
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