Re: forwarded message from Peng-Sheng Chen

[Brian Gough <bjg at network-theory dot co dot uk>]

 >    If I want to get all solutions (not only one solution), how
 >    to do it ?
 >    (some equations exist many solutions.)
 >    Thanks very much.
 > 
 > 

There should be some information on the web about solving
"underdetermined systems" using the SVD.  If not I think there is a
section in Golub and Van Loan's book on 'Matrix Computations' about
it.

regards,

Brian Gough

								Ps. Chen
 > > -----Original Message-----
 > > From: Brian Gough [mailto:bjg@network-theory.co.uk]
 > > Sent: Wednesday, May 08, 2002 5:23 AM
 > > To: Peng-Sheng Chen
 > > Cc: gsl-discuss@sources.redhat.com
 > > Subject: Re: FW: GSL support "left division \ " ?
 > >=20
 > > Peng-Sheng Chen writes:
 > >  > Hello: =A0 =A0=A0 There is an equation: Ax =3D B.  =A0=A0 A is =
 > m-by-n matrix.
 > >  > =A0=A0 x is n vector.  =A0=A0 B is m vector.  =A0=A0 The condition =
 > is m >=3D n,
 > >  > that is =A0=A0 we have equations more than unknown variable.  =A0 =
 > =A0=A0 In
 > >  > matlab, it support a operator =93left divide \ =94 to manipulate
 > >  > =A0=A0 the equations. In GSL, how to compute x ? (multidimention
 > >  > root-finding?)  =A0=A0 Thanks very much.
 > >=20
 > > For overdetermined systems you can find the least-squares solution
 > > using gsl_linalg_QR_lssolve or gsl_linalg_SV_solve, described in the
 > > "Linear Algebra" chapter of the manual.
 > >=20
 > > regards
 > > Brian Gough
 > >=20
 >