Secant Method algorithm in Matlab

Secant Method algorithm in Matlab :

function [xvect,xdif,fx,nit] = secant(x1,x0,nmax,fun,toll); % SECANT Do the secant iteration to find the zeros of the given % inline scalar function and its derivative. % [XVEC,XDIF,FX,NIT] = SECANT(X1,X0,NMAX,FUN,TOLL) % Input:x0 and x1 starting value % nmax: maximum number of iteration % toll: tolerance, default is 1e-10 % fun: given inline function % % Output: xvect: stores values in all iterations (arg) % xdif : difference between two successive values % (arg) % fx: stores function values in all iterations % nit: number of iteration required % % Examples: % fun=inline('x^3+x^2-4'); x0=0.3;x1=0.5; nmax=100; % fun=inline('x^5+10*x^2-9*x+10'); % Author: Bishnu Lamichhane, University of Stuttgart if (nargin==4) toll=1e-10; end x=x1; fx1=feval(fun,x); xvect=[x]; fx=[fx1]; x=x0; fx0=feval(fun,x); xvect=[xvect;x];fx=[fx;fx0];err=toll+1;nit=0;xdif=[]; while(nit<nmax & err>toll) nit=nit+1; if (abs(fx0-fx1)<eps) err=toll*1e-10; disp('Stop for vanishing dfun'); else x=x0-fx0*(x0-x1)/(fx0-fx1); xvect=[xvect;x]; fnew=feval(fun,x); fx=[fx;fnew]; err=abs(x0-x); xdif=[xdif;err]; x1=x0;fx1=fx0;x0=x;fx0=fnew; end; end; n=1:nit; plot(n, xdif, '-*'); title(['Plot of error with respect to iteration, f(x)=',char(fun)]); xc = get(gca,'XLim'); yc = get(gca,'YLim'); xc = (xc(1)+xc(2))/2; text(xc,yc(2)*0.9,['x_{zero} = ',num2str(x)], ... 'HorizontalAlignment', 'center');