[SciPy-User] Large banded matrix least squares solution

Charles R Harris charlesr.harris@gmail....
Wed Mar 16 15:02:57 CDT 2011

On Wed, Mar 16, 2011 at 1:53 PM, J. David Lee <johnl@cs.wisc.edu> wrote:

> Hello.
> I'm trying to find a least squares solution to a system Ax=b, where A is
> a lower diagonal, banded matrix. The entries of A on a given diagonal
> are all identical, with about 300 unique values, and A can be quite
> large, on the order of 1e6 rows and columns.
So this is sort of a convolution? Do you need exact, or will somewhat
approximate do? I think you can probably do something useful with an fft.

scipy.sparse.linalg.lsqr works on smaller examples, up to a few thousand
> rows and columns, but not much larger. It is also very time consuming to
> construct A, though I'm sure there must be a fast way to do that.
> Given the amount of symmetry in the problem, I suspect there is a fast
> way to calculate the result, or perhaps another way to solve the problem
> entirely.
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