[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


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

     if ||Y1||<||Y||
            damp = damp/2;

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



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