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Re: Find non-trivial solution
- From: Brian Gough <bjg at network-theory dot co dot uk>
- To: wwfarch at rochester dot rr dot com
- Cc: gsl-discuss at sources dot redhat dot com
- Date: Tue, 08 Aug 2006 18:15:00 +0100
- Subject: Re: Find non-trivial solution
- References: <c5f3c0c04d8b1.4d8b1c5f3c0c0@nyroc.rr.com>
- Reply-to: gsl-discuss at sourceware dot org
At Thu, 03 Aug 2006 14:43:49 -0400,
wwfarch@rochester.rr.com wrote:
> I'm having an issue with GSL and solving homogeneous systems. In
> particular I have an equation of the form: Av = 0 where A is an Nx6
> matrix, v is a vector (size 6) and 0 represents a zero vector.
>
> Regardless of N when I solve for v I always get the trivial solution (v
> = 0). Is there a way to force GSL to provide a non-trivial solution?
> Once I have a non-trivial solution I can scale as I need to for my
> application. As a note, when N>6 I solve with a least squares solution.
> I've tried QR and SVD decompositions.
Hello,
The _solve functions do back-substitution so will always give v=0 for
a zero rhs. If you want to find the null space of A, use the SVD to
get a basis for it from the columns of V corresponding to the zero
singular values.
--
Brian Gough
Network Theory Ltd,
Publishing the GSL Manual - http://www.network-theory.co.uk/gsl/manual/