dampednewton.m

Nonlinear Problem Files Collection

function [] = dampedNewton(f,Df,x0,maxite);

format compact

xMax=1.5*abs(x0);
xMin=-xMax;
dt= (xMax-xMin)/100;

yMax=abs(feval(f,xMax));

t = xMin:dt:xMax;
plot(t,feval(f,t),'k-');

axis([xMin xMax -yMax yMax]);

hold on;
plot([xMin xMax],[0 0],'k-');
hold on;
plot([0 0],[-yMax yMax],'k-');

x(1)=x0; k=0; 
disp(sprintf('x_%d=%f',k/2,x(k+1)))
y(1)=0;

for k=2:2:2*maxite

   x(k)=x(k-1);
   y(k)=feval(f,x(k));

   dx=-feval(f,x(k))/feval(Df,x(k));

   lambda=2;
   lambdaMin=1.e-10;
   ddx=2*dx;

   while abs(ddx)>(1-lambda/2.)*abs(dx)
     lambda=lambda/2;
     if lambda<lambdaMin  lambda=-1; disp('lambda zu klein'); break; end;

     z=x(k-1)+lambda*dx;
     ddx=-feval(f,z)/feval(Df,x(k));
   end;
  
   if lambda<0 break; 
   else
     waitforbuttonpress;
     x(k+1)=x(k)+lambda*dx;
     disp(sprintf('x_%d= %f    lambda=%f',k/2,x(k+1),lambda));
     y(k+1)=0;
     plot(x,y,'r*-');
   end;

end;

if lambda<0 displ('Daempfungsparameter zu klein'); end;
hold off;