# Sparse matrix inverse with reduced bandwidth

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-rho*B, where 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?