🚀 go-pugleaf

  In article <C14IEJ.343.1@cs.cmu.edu> bs36+@EDRC.CMU.EDU (Boyd T
  Safrit) writes:

  I have been working with an equation solver with the
  idea of adding in the capability of condition number estimation.  My
  problem is this: I usually have a set of m equations in n variables,
  where n > m.  The remaining variables are "fixed" by the user.  We
  have had problems with some of the systems being ill conditioned. One
  of the cures we have identified is for the user to pick new degrees of
  freedom, or swapping some of the fixed variables in and some of the
  unfixed variables out of the factorization (we use something like
  Gaussian, but are looking at others.)  There are articles on
  incremental estimation that mention applications te kinds of problems.
  I would like to be able to give the user the proper set of variables
  to swap in and out, with the idea of decreasing the conditioning of
  the resulting system.  Does anyone have any information on this kind
  of problem?  Thanks in advance.  Boyd Safrit

The problem of variable selection was once a hot topic in statistics,
though the case considered was $m>n$; i.e., regression.  However,
for your case a QR~decomposition with column pivoting should be
adequate.  The LINPACK routines sqrdc and sqrsl should suit your
application.

Pete Stewart