I have a sparse symmetric matrix of dimension
1393x1393 (8308 no zero elements), with bandwidth 1380. By Cuthill–McKee algorithm, I could achieve a new matrix with bandwidth 89. If we call this matrix
B, then I'm interested in calculate the inverse
I is a diagonal matrix and
rho is a parameter updated in my MCMC algorithm. I need to calculate matrix inverse many times (during MCMC) and someone told me by reducing the matrix bandwidth, I can obtain faster matrix inverse.
I am using R as my programming language. The
solve function is used to calculate the inverse of a matrix. I noticed no difference when calculating the inverse of a sparse matrix with bandwidth 1380 or bandwidth 89.
I guess I need some explicit commands/options in order to take advantage of the bandwidth reduction, but I don't know what keywords should I aim at. Can anyone give me some suggestions?
A former post with more information.