0
$\begingroup$

So I'm trying to invert a matrix of the $\begin{pmatrix} A & B \\ C & D \end{pmatrix}$ where $A$ and $D$ are square, $D$ is much larger than $A$, and $D$ is diagonal. $A$ $B$ and $C$ have no particular structure. Is there a fast way to do this that takes advantage of D's being diagonal?

  • 0
    With diagonal matrices being [very easy to invert](http://www.ee.oulu.fi/~mpa/matreng/eem1_5-3.htm), the second version of the formula at [Wikipedia Blockwise Inversion](https://en.wikipedia.org/wiki/Invertible_matrix#Blockwise_inversion) should help2012-04-29
  • 0
    Also, you can write your matrix as $D'+A'$, where $D'$ is diagonal and $A'$ is sparse. You may then use the [matrix inversion lemma](http://en.wikipedia.org/wiki/Woodbury_matrix_identity) combined with blockwise inversion for potential speedups. You may also want to look into schemes for inverting sparse matrices.2012-04-29

2 Answers 2