b'\n_START_ARTICLE_\nMetoda coardei\n_START_PARAGRAPH_\n\xc3\x8en analiz\xc4\x83 numeric\xc4\x83, metoda coardei (sau metoda falsei pozi\xc8\x9bii, metoda falsi) este o metod\xc4\x83 de determinare a r\xc4\x83d\xc4\x83cinii unei func\xc8\x9bii pe un interval.\n_START_SECTION_\nIstorie\n_START_PARAGRAPH_\nCele mai vechi documente care atest\xc4\x83 cunoa\xc8\x99terea \xc8\x99i \xc3\xaen\xc8\x9belegerea metodei falsei pozi\xc8\x9bii dateaz\xc4\x83 cu aproxima\xc8\x9bie din anul 200 \xc3\xae.Hr. \xc8\x99i 200 \xc3\xae.Hr.. Metoda a fost g\xc4\x83sit\xc4\x83 \xc3\xaentr-un text antic chinez numit \xe2\x80\x9eNou\xc4\x83 capitole despre arta matematicii\xe2\x80\x9d. \xc3\x8en acest text, cu toate acestea, exemple de probleme care aplic\xc4\x83 metoda falsei pozi\xc8\x9bii sunt doar la ecua\xc8\x9bii liniare \xc8\x99i solu\xc8\x9biile sunt atinse \xc3\xaentr-o singur\xc4\x83 etap\xc4\x83._NEWLINE_\xc3\x8en Occident, aceast\xc4\x83 metod\xc4\x83 a fost utilizat pe scar\xc4\x83 larg\xc4\x83 de c\xc4\x83tre matematicienii Fibonacci, Luca Pacioli \xc8\x99i Robert Recorde.\n_START_SECTION_\nPseudocod\n_START_PARAGRAPH_\n\'\'N\'\' \xe2\x86\x90 1_NEWLINE_ While \'\'N\'\' \xe2\x89\xa4 \'\'NMAX\'\' _NEWLINE_{ _NEWLINE_   \'\'c\'\' \xe2\x86\x90 \'\'a\'\'-\'\'f(a)\'\'*(\'\'b\'\' - \'\'a\'\')/(\'\'f(b)\'\' - \'\'f(a)\'\') _NEWLINE_   If (\'\'f\'\'(\'\'c\'\') = 0 or (\'\'b\'\' \xe2\x80\x93 \'\'a\'\')/2 < \'\'TOL\'\' then _NEWLINE_{ _NEWLINE_     Output(\'\'c\'\')_NEWLINE_     Stop_NEWLINE_}_NEWLINE_   \'\'N\'\' \xe2\x86\x90 \'\'N\'\' + 1 _NEWLINE_   If sign(\'\'f\'\'(\'\'c\'\')) = sign(\'\'f\'\'(\'\'a\'\')) then \'\'a\'\' \xe2\x86\x90 \'\'c\'\' else \'\'b\'\' \xe2\x86\x90 \'\'c\'\' _NEWLINE_ }_NEWLINE_ Output("Algoritmul nu determin\xc4\x83 solu\xc8\x9bia \xc3\xaen num\xc4\x83rul maxim de itera\xc8\x9bii.") _NEWLINE_In limbajul C_NEWLINE_#include<iostream.h>#include<math.h>#define eps 0.00000000001#define iter 200_NEWLINE_ _NEWLINE_double f(double x){return x*x*x-2*x*x*cos(x)+x-3;}_NEWLINE_ _NEWLINE_void main(){unsigned char i;double x,x0,x1,a,b,y;_NEWLINE_cout<<"a=";cin>>a;cout<<"b=";cin>>b;_NEWLINE_i=0;x0=a;x1=b;x=x0;y=f(x);if (f(x0)*f(x1)<0)_NEWLINE_{_NEWLINE_while ( (i<=iter) && ((y<-eps) || (y>eps)) )_NEWLINE_{_NEWLINE_x=x0-f(x0)*(x1-x0)/(f(x1)-f(x0));_NEWLINE_y=f(x);_NEWLINE_if (f(x0)*y<0) x1=x; _NEWLINE_else x0=x;_NEWLINE_cout<<"\\n\\nf("<<x<<")="<<f(x)<<" la iteratia "<<(int)i;_NEWLINE_i++;_NEWLINE_}_NEWLINE_if (i>iter) cout<<"problema nu se poate rezolva in nr.maxim de iteratii";_NEWLINE_} else cout<<"interval invalid";}'