Algorithme de la Méthode de la Sécante en Matlab

Algorithme de la Méthode de la Sécante en Matlab :

function [x,fx,xx] = secant(f,x0,TolX,MaxIter,varargin) % solve f(x) = 0 by using the secant method. %input : f = ftn to be given as a string ’f’ if defined in an M-file % x0 = the initial guess of the solution % TolX = the upper limit of |x(k) - x(k - 1)| % MaxIter = the maximum # of iteration %output: x = the point which the algorithm has reached % fx = f(x(last)), xx = the history of x h = 1e-4; h2 = 2*h; TolFun=eps; xx(1) = x0; fx = feval(f,x0,varargin{:}); for k = 1: MaxIter if k <= 1, dfdx = (feval(f,xx(k) + h,varargin{:})-... feval(f,xx(k) - h,varargin{:}))/h2; else dfdx = (fx - fx0)/dx; end dx = -fx/dfdx; xx(k + 1) = xx(k) + dx; %Eq.(4.5.2) fx0 = fx; fx = feval(f,xx(k+1)); if abs(fx) < TolFun | abs(dx) < TolX, break; end end x = xx(k + 1); if k == MaxIter, fprintf(’The best in %d iterations\n’,MaxIter), end