[petsc-dev] How to implement the damped Newton method

[Lulu Liu]

X is the current approximate solution, Y is the Newton direction

Step 1. the unknown X=[phi,omega,S], the third component S in [0,1]. Hence,
we firstly compute a multiplier alpha such that

X1= X-alpha*Y, and the component S of X1 is still in [0,1].
In step1, we need access the component S to calculate multiplier.

Step 2. Let the damping factor damp=1;

for n=1:N

    lambda=alpha*damp;
    X1=X-lambda*Y;

     Solve J(X1)Y1 = F(X1);

     if ||Y1||<||Y||
           break;
      else
            damp = damp/2;
       end
endfor

the norm || || is weighted norm, and we need access each component and
compute some weights based on each component.


How to implement the damped Newton method above? Is it a easier way to do
it?

Thanks!

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