commit bcea18df74f0e878ec0c8b3654cdccc5e3e5e556 parent d7010e8e419eb9063d94dde21883b5ed3c92fac6 Author: Silas Brack <s174433@student.dtu.dk> Date: Wed, 1 Feb 2023 20:01:23 +0100 Fixt Diffstat:
| M | chapters/sampling.tex | | | 2 | +- |
1 file changed, 1 insertion(+), 1 deletion(-)
diff --git a/chapters/sampling.tex b/chapters/sampling.tex @@ -343,7 +343,7 @@ However, this preconditioner will be very expensive to compute, since it effecti \subsection{Using the Woodbury Matrix Identity}[Woodbury] \label{sec:woodbury-preconditioner} -The Woodbury matrix identity is a useful identity for computing the inverse of a matrix which is the sum of two matrices of which one is low-rank and the other can easily be inverted.\sidenote{EXPLAIN WOODBURY MATRIX IDENTITY MORE MAYBE?} +The Woodbury matrix identity is a useful identity for computing the inverse of a matrix which is the sum of two matrices of which one is low-rank and the other can easily be inverted.\sidenote{SHOULD I EXPLAIN WOODBURY MATRIX IDENTITY MORE MAYBE?} This identity can be used to compute the inverse of the GGN matrix with the prior precision, which is given by \begin{align} \left( \alpha \identity + \bm J\T \bm H \bm J \right)^{-1} \bm v = \alpha^{-1} \identity - \alpha^{-2} \bm J\T \left( \bm H^{-1} + \alpha^{-1} \bm J \bm J\T \right)^{-1} \bm J