Re: manipulating block diagonal matrices
- To: mathgroup at smc.vnet.net
- Subject: [mg37620] Re: [mg37587] manipulating block diagonal matrices
- From: Sseziwa Mukasa <mukasa at jeol.com>
- Date: Wed, 6 Nov 2002 06:58:08 -0500 (EST)
- Sender: owner-wri-mathgroup at wolfram.com
On Tuesday, November 5, 2002, at 05:05 AM, David E. Burmaster wrote: > Dear MathGroup, > > Can anyone suggest efficient algorithms for calculating either or both > of > these? > > (i) the inverse and (ii) the determinant of a block diagonal matrix? > > Let blocki for i = 1, 2,..., n denote each of the square matrices > along the > diagonal of a large block diagonal matrix. > > In my situation, the blocki matrices do not have a common size; a > typical > blocki has dimensions in the range 6x6 to 20x20. > > In my situation, n is approx 1,000. > > In other words, the full block diagonal matrix has large dimensions -- > but > it is sparse in a highly structured way. > If you are not storing the entire array but only the nonzero blocks then the fastest method would be to take the inverses of each block independently. The product of the determinants of the blocks is the determinant of the matrix also. Regards, Ssezi