newthorn.m

various matlab programs to slove various problems

function [xn,iter,root,itrefin]=newthorn(A,n,toll,x0,nmax,iref)
apoly=A;
for i=1:n, it=1; xn(it,i)=x0+sqrt(-1)*x0; err=toll+1; Ndeg=n-i+1;
  if (Ndeg == 1), it=it+1; xn(it,i)=-A(2)/A(1);
  else
     while (it < nmax & err > toll),
        [px,B]=horner(A,Ndeg,xn(it,i)); 
        [pdx,C]=horner(B,Ndeg-1,xn(it,i));
        it=it+1; if (pdx ~=0), xn(it,i)=xn(it-1,i)-px/pdx;
        err=max(abs(xn(it,i)-xn(it-1,i)),abs(px));
        else, 
            disp(' Stop due to a vanishing p'' '); 
            err=0; xn(it,i)=xn(it-1,i);
        end
     end
  end
  A=B;
  if (iref==1), alfa=xn(it,i); itr=1; err=toll+1; 
     while ((err > toll*1e-3) & (itr < nmax))
       [px,B]=horner(apoly,n,alfa); 
       [pdx,C]=horner(B,n-1,alfa); itr=itr+1;
       if (pdx~=0)
          alfa2=alfa-px/pdx; 
          err=max(abs(alfa2-alfa),abs(px)); alfa=alfa2;
       else, 
          disp(' Stop due to a vanishing p'' '); err=0; 
       end
     end; itrefin(i)=itr-1; xn(it,i)=alfa;
  end   
  iter(i)=it-1; root(i)=xn(it,i); x0=root(i);
end