Algorithme de la Méthode de la Position Fausse en Matlab

Algorithme de la Méthode de la Position Fausse en Matlab :

function [x,err,xx] = falsp(f,a,b,TolX,MaxIter) %bisct.m to solve f(x)=0 by using the false position method. %input : f = ftn to be given as a string ’f’ if defined in an M-file % a/b = initial left/right point of the solution interval % TolX = upperbound of error(max(|x(k)-a|,|b-x(k)|)) % MaxIter = maximum # of iterations %output: x = point which the algorithm has reached % err = max(x(last)-a|,|b-x(last)|) % xx = history of x TolFun = eps; fa = feval(f,a); fb=feval(f,b); if fa*fb > 0, error(’We must have f(a)f(b)<0!’); end for k = 1: MaxIter xx(k) = (a*fb-b*fa)/(fb-fa); %Eq.(4.3.1) fx = feval(f,xx(k)); err = max(abs(xx(k) - a),abs(b - xx(k))); if abs(fx) < TolFun | err<TolX, break; elseif fx*fa > 0, a = xx(k); fa = fx; else b = xx(k); fb = fx; end end x = xx(k); if k == MaxIter, fprintf(’The best in %d iterations\n’,MaxIter), end