secant.m

In numerical analysis, the secant method is a root-finding algorithm that uses a succession of roots

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');