Sparse solver for non-square regressor matrix.
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Paulo Cerqueira
on 5 Mar 2020
Edited: Paulo Cerqueira
on 13 Mar 2020
When using the backslash operator to solve the least squares problem for x, where A is highly sparse and non-square, MATLAB seems to apply a fast procedure that scales quite well with the size of A, as opposed to what one would expect from a standard QR-solver for full matrices.
However, the documentation is not quite clear with regard to what the specific procedure is when the regressor is sparse but not square, and I'd like to have a notion of its computational complexity.
I would like to know if someone could provide the article/book on which the procedure applied by MATLAB's backslash is based when the regressor A is sparse and not square.
Regards.
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David Goodmanson
on 6 Mar 2020
Edited: David Goodmanson
on 6 Mar 2020
Hi Paulo,
see 'doc mldivide' which is really a more obscure reference than it should be. The flowchart there says nonsquare sparse uses QR, although they do not say anything more. A lot of their core algorithms they play pretty close to the vest.
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