R help - Jul 2012 - Fast trace of inverse

Suppose I have a square matrix A like the toy below

set.seed(1234)
(A <- matrix(rnorm(9), nrow = 3))

I want to trace of the inverse of A. I could do
> sum(diag(solve(A)))
[1] 1.259641

Or I could also do
> sum(1/eigen(A)$values)
[1] 1.259641+0i

Now, my actual problem involves a very large, square dense matrix. Is step 2
still the best R-ish way of doing this or is there a smarter and fast
implementation for such cases?

Harold


	[[alternative HTML version deleted]]

Hi Harold,

There are algorithms that provide approximations to the trace of inverse of
large SPD matrices.  These use Gaussian quadrature.  A couple of paper are worth
noting:  Bai & Golub, and a recent paper by Meurant (2009) that improves on
the Bai-Golub quadrature method.

I have not implemented this in R, but it may be worth considering.

I am not sure if there are good solutions for general, unstructured square
matrices.

Ravi

Ravi Varadhan, Ph.D.
Assistant Professor
The Center on Aging and Health
Division of Geriatric Medicine & Gerontology
Johns Hopkins University
rvaradhan at jhmi.edu<mailto:rvaradhan at jhmi.edu>
410-502-2619

-------------- next part --------------
A non-text attachment was scrubbed...
Name: Meurant_2009.pdf
Type: application/pdf
Size: 117720 bytes
Desc: Meurant_2009.pdf
URL:
<https://stat.ethz.ch/pipermail/r-help/attachments/20120706/b44c8e8d/attachment.pdf>