5
$\begingroup$

I wish to solve the following set of coupled eigenvalue equations. How should I do it?

For real matrices $A$,$B$,$D$ and vectors $x \in R^m$, $y \in R^n$ $$ A x + B y = \lambda x $$ $$ B^T x + D y = \mu y $$ where, $A$ and $D$ are symmetric.

Background:

I am trying to solve the following optimization problem:

$$ \min x^T A x + y^T D y + x^T By $$ $$ \textrm{such that } \, x^T x = 1 , y^T y = 1 $$ This leads to the above eigenvalue problem. $\lambda$ and $\mu$ are the Langrangian parameters for the constraints.

EDIT: I need to actually find numerical solutions for these equations given $A$, $B$, $D$

  • 0
    From the optimization, I just realized I want to maximize $\lambda + \mu$2011-06-25

4 Answers 4