rank-defficient under-determined system

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rank-defficient under-determined system

Postby cuongny » Tue Nov 29, 2011 12:43 pm

I am trying to solve an under-determined system of equation (more variables than equations)

Routines SGELS/DGELS assumes that the matrix is full-rank, what happens if the A matrix is rank defficient?
Will it thow any erros or will it still proceed solving the linear system?

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Joined: Mon Nov 28, 2011 7:32 pm

Re: rank-defficient under-determined system

Postby sven » Tue Nov 29, 2011 1:14 pm

If you suspect that your matrix may be rank deficient then you should use one of the routines


The first two use the singular value decomposition (SVD) and the third uses the complete orthogonal decomposition.
The SVD is the most reliable for rank detection, but the complete orthogonal decomposition is likely to be faster.

S/DGELS is only intended for full rank problems.

See the LAPACK Users' Guide, Section 2.3.2 Linear Least Squares (LLS) Problems, for further information:


Sven Hammarling.
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Joined: Wed Dec 22, 2004 4:28 am

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