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Metoda coardelor
1.
2. Metoda este utilizata pentru gasirea radacinii
aproximative a ecuatiei f(x)=0 izolate intr-un
interval [a,b] in cazul in care f(a)*f(b)<0 cu
aproximarea prestabilita
Se considera ecuata f(x)=0. Functia f(x) este
continua pe [a,b]. Presupunem ca in urma
unui proces de separare a radacinilor ecuatia
f(x)=0 are cel mult o radacina in [a,b].
Prin notam radacina ecuatiei pe [a,b]
3. Intervalele succesive [a1,b1]
,[a2,b2]…[ai,bi] se obtin prin impartirea
intervalului anterior in raportul
f(ai-1)/f(bi-1);
Medota secantei este ecivalenta cu
inlocuirea f(x),prin coarda care trece
prin punctele (ai,f(ai)) si (bi,f(bi)).
4. Fie f’’(x)>0,unde a X b(cazul f’’(x)<0 se reduce la cazul
analizat daca ecuatia este rescrisa in forma – f(x)=0.
Atunci curba y=f(x) este concava si se afla mai jos de
coarda sa Ab.Sunt posibile doua situatii:
f(a)>0 fig.1 f(a)<0 fig 2
5. Nemiscat este acel capat al intervalului pentru
care semnul functiei f(x) coincide cu semnul
derivatei de ordinul doi f’’(x);
Aproximari consecutive xn se afla in acea parte
de radacina unde functia f(x) are semnul opus
semnului derivatei de ordinul doi f’’(x).