[R] Invert a positive definite symmetric Block Toeplitz Matrix

Alexander Braumann alexander.braumann at tuwien.ac.at
Mon Jun 17 17:28:17 CEST 2013

Is there a function in r that let's you efficiently invert a positive 
definite symmetric Block Toeplitz matrix? My matrices are the covariance 
matrices of observations of a multivariate time series and can be 
1000*1000 or larger.

I know the package 'ltsa' which seems to use the Trench algorithm to 
compute the inverse of a Toeplitz matrix. I am looking for a so to say 
"multivariate" version of that. I found the Block Levinson algorithm in 
Matlab, but didn't find any version of it in R.

My problem is part of a bigger problem, which is first computing the 
log-likelihood of the observations Y_T=(Y_1, ..., Y_T) of an 
n-dimensional time-series (Y_t) and second, finding an approximation of 
the MLE by using e.g. the BFGS algorithm.

As this algorithm does not function properly (no convergence), I thought 
that maybe the inversion of the big covariance matrix EY_T Y_T' may be a 
source a trouble.

Thanks for inputs in advance!

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