Cholesky decompositon of spd BandedBlockBanded matrices

[TSGut]

How much work would it be to get cholesky working on infinite spd BandedBlockBanded matrices?

I'm wondering whether decomposition methods also allow for interesting weight OPs in higher dimension and want to test this with the Jacobi matrices on the Zernike disk. I can always experiment with finite blocks for now, just wanted to put the thought out there.

[dlfivefifty]

First you would need to finish block Cholesky which was started here:

https://github.com/JuliaArrays/BlockArrays.jl/pull/126

As you can see it uses LAPACK's cholesky. This should work for BlockBandedMatrix. I believe then it would be pretty easy to get the infinite case working.

A more interesting question is how to take advantage of structure in BandedBlockBandedMatrix. Since Cholesky has a simple rank update formula (which I believe is stable, unlike Woodbury formula) it is possible to

1. parallelise the Cholesky factorization.
2. Reduce complexity to O(N^(3/2)) for N unknowns.

But this is a bigger undertaking.