Calculating the exponential matrix.

Hi all,

I have a matrix exponential , where:

In specific, a is an arbitrary constant, I is the identity matrix, and A, B are tri-diagonal matrices where their entries range in the 1e5 and 1e1 orders of magnitude respectively. Since I am calculating the exponential matrix using expm, presumably due to the large difference in the orders of magnitude of the two block matrices A and B, the procedure returns large errors. Their condition numbers of these matrices are also in the order of 1e10, which is not very good....

I was therefore wondering if there are any identities or properties of the exponential matrix where I can take advangage in order to perform the calculation of the exponential matrix more accurately, such as splitting the matrix M and performing individual matrix exponentiations.

Thanks for your help in advance.

P.S. I have read up on the Cleve's corner, which seems to have interesting information. Didn't magage to obtain an answer on the above though, as its a bit too specific to the problem that I am facing.

I also realise that this might be one of the cases of 'wishful thinking' where I am just screwed and I have to deal with this matrix no matter what, unless I drastically change my approach such that I don't have to perform the exponentiation in the first place.