[petsc-dev] How to implement the damped Newton method
Lulu Liu
lulu.liu at kaust.edu.sa
Sat Feb 7 02:39:30 CST 2015
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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