Newton Method algorithm in Matlab

Newton Method algorithm in Matlab :

function [xvect,xdif,fx,nit]=mynewton(x0,nmax,fun,dfun,toll); % MYNEWTON Do the newton iteration to find the zeros of the given % inline scalar function. % [XVEC,XDIF,FX,NIT] = MYNEWTON(X0,NMAX,FUN,DFUN,TOLL) % Input: x0: starting value % nmax: maximum number of iteration % toll: tolerance, default is 1e-10 % fun: given inline function % dfun: derivative of the function given as inline % function % % Output: xvect: stores values in all iterations (arg) % xdif: difference between two consequent values (arg) % fx: stores function values in all iterations % nit: number of iteration required % % Examples: % The first examples converge to unique zero % fun=inline('x^3+x^2-4'); x0=0.3; nmax=100; % dfun=inline('3*x^2+2*x'); % % fun=inline('x^4+x^3-5*x-12'); % dfun=inline('4*x^3+3*x^2-5'); % % fun=inline('x^5+10*x^2-9*x+10'); % dfun=inline('5*x^4+20*x-9'); % % Examples where different starting values converge to % different zeros % fun=inline('x^2-4*sin(x)'); % dfun=inline('2*x-4*cos(x)'); % % fun=inline('x^3+x^2*(cos(x))^2-4'); % dfun=inline('(3*x^2+2*x*cos(x)^2-2*x^2*cos(x)*sin(x))'); % Author: Bishnu Lamichhane, University of Stuttgart if (nargin==4) toll=1e-10; end err=toll+1; nit=0; xvect=x0;x=x0;fx=feval(fun,x);xdif=[]; while(nit<nmax & err>toll) nit=nit+1; x=xvect(nit);dfx=feval(dfun,x); if (dfx==0), err=toll*1e-10; disp('Stop for vanishing dfun'); else, xn=x-fx(nit)/dfx;err=abs(xn-x);xdif=[xdif;err]; x=xn;xvect=[xvect;x];fx=[fx;feval(fun,x)]; 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),'; x_{start} =' , ... num2str(x0)], 'HorizontalAlignment', 'center');