When solving systems of non-linear equations using Newton's method, it is often observed that the system has an independent sub-system, e.g. :

$$ f(x,y) = 0 $$ $$ g(x,y) = 0 $$ $$ h(x,y,z) = 0 $$

If I am not mistaken, you can (and should) solve first for $x$ and $y$ and then subsequently solve for $z$. Now when the dimension of the system increases, it is not so easy to spot such independent sub-systems. Are there algorithms adapted to this issue ?

In my specific case, the Jacobian of the system has a fixed structure so even a slow algorithm for detection would be largely beneficial when solving the non-linear system using Newton's method. I feel that this is a common topic in solving systems of equations, so I am open to be redirected to additional ressources that are relevant.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.