[SciPy-User] Large banded matrix least squares solution

nicky van foreest vanforeest@gmail....
Wed Mar 16 16:47:33 CDT 2011


Hi,

On 16 March 2011 20:53, 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.

Perhaps I get you wrong, but it appears to me that a_11 x_1 =b_1 (the
system is lower diagonal) fixes x_1 uniquely. The second line of A
then fixes x_2 etc. Hence, this system is not overspecified, and a
least squares approach does not seems to make sense. Least squares
becomes interesting when A has more columns than rows, i.e., is
overspecified.

NIcky

>
> 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.
>
> Thank you for your help,
>
> David Lee
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