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Inverting banded-block matrices. [message #36313]

Thu, 28 August 2003 16:07

James Kuyper
Messages: 425
Registered: March 2000

Senior Member

I've got a problem where I have to calculate g = C D^-1 f, where g and f
are vectors, and C and D are matrices. C has m by m blocks, each of
which is itself an n by n matrix. It is banded, with k non-zero
co-diagonals above and below the main diagnal, both at the block level
and within each block. C[i,j] ge 0. Every statement I've made about C
also applies to D.
For the sake of definiteness, m=10, n=1354, k = 3.

This seems like it should be a pretty common type of matrix structure
for problems involving 2-D grids. I could solve this by explicitly
inverting a m*n by m*n matrix. However, I would assume that there are
existing routines somewhere which can take good advantage of the
sparseness of these matrices to speed up the calculations considerably.
Could anyone point me at such routines?

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