Is there a name and common technique for such equations, where $A$ and $B$ are matrices and $x$ a vector?
$Ax+f(\lambda)Bx=g(\lambda)x$.
$\begingroup$
$\endgroup$
2
asked Jan 4, 2013 at 12:11
-
$\begingroup$ from the way this nonlinear eigenvalue problem looks, i presume both $\lambda$ and $x$ are "unknowns"? $\endgroup$– SuvritJan 4, 2013 at 12:35
-
$\begingroup$ @Suvrit: yes, $\lambda$ is a scalar. $\endgroup$– Felix GoldbergJan 4, 2013 at 12:51
Add a comment
|
1 Answer
$\begingroup$
$\endgroup$
Akin to my comment, this equation can be called a nonlinear generalized eigenvalue problem. Usually, $f$ and $g$ are polynomials in $\lambda$, but more general nonlinearities might be allowed. In general, I doubt there will be robust, globally convergent method for this equation that gets all the solutions. The talk or this paper might be good starting points (see especially the paper).
