aitken.m

various matlab programs to slove various problems

function [xvect,xdif,fx,nit]=aitken(x0,nmax,toll,phi,fun)
nit=0; xvect=[x0]; x=x0; fxn=eval(fun); 
fx=[fxn]; xdif=[]; err=toll+1;
while err >= toll & nit <= nmax
  nit=nit+1; xv=xvect(nit); x=xv; phix=eval(phi); 
  x=phix; phixx=eval(phi); den=phixx-2*phix+xv;
  if den == 0,  err=toll*1.e-01; 
  else, xn=(xv*phixx-phix^2)/den; xvect=[xvect; xn];
     xdif=[xdif; abs(xn-xv)]; x=xn; fxn=abs(eval(fun)); 
     fx=[fx; fxn]; err=fxn;
  end 
end