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Aproximarea functionalelor liniare

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Introducere<br />

Derivare numerică<br />

Integrare numerică<br />

Cuadraturi adaptive<br />

Cuadraturi . . .<br />

Cuadraturi . . .<br />

Formule . . .<br />

Home Page<br />

Title Page<br />

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Page 30 of 58<br />

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Close<br />

Quit<br />

Să presupunem că<br />

metint(a, b : real; f : functie, n : integer) : real<br />

este o funct¸ie care aproximează b<br />

f(x)dx folosind o cuadratură<br />

a<br />

repetată cu n subintervale. Pentru m se alege o valoare mică (4<br />

sau 5).<br />

Algoritmul 1 Cuadratură adaptivă<br />

Intrare: f - funct¸ia de integrat, a, b - limitele de integrare, ε -<br />

tolerant¸a, metint - o cuadratură repetată<br />

Ie¸sire: valoarea integralei<br />

function adapt(f, a, b, ε, metint)<br />

if |metint(a, b, f, 2m) − metint(a, b, f, m)| < ε then<br />

adapt := metint(a, b, f, 2m);<br />

else<br />

adapt := adapt(f, a, (a + b)/2, ε, metint) + adapt(f, (a +<br />

b)/2, b, ε, metint);<br />

end if<br />

Structura algoritmului: DIVIDE AND CONQUER.

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