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Re: [Help-glpk] numerical instability

From: Meketon, Marc
Subject: Re: [Help-glpk] numerical instability
Date: Tue, 12 Jul 2011 07:32:03 -0500

I thought that the three different basis factorization methods that Andrew developed were meant to improve numerical stability (at the cost of speed).  Has anyone tried these?

Using "glpsol" the options are (this comes from the glpsol --help usage statement):

LP basis factorization options:
   --luf             LU + Forrest-Tomlin update
                     (faster, less stable; default)
   --cbg             LU + Schur complement + Bartels-Golub update
                     (slower, more stable)
   --cgr             LU + Schur complement + Givens rotation update
                     (slower, more stable)

And using the C library the options to run these factorizations are found in the glp_bfcp control structure.  The below comes from the GLPK documentation.

int type (default: GLP_BF_FT)
    Basis factorization type:
    GLP_BF_FT - LU + Forrest{Tomlin update;
    GLP_BF_BG - LU + Schur complement + Bartels-Golub update;
    GLP_BF_GR - LU + Schur complement + Givens rotation update.
    In case of GLP_BF_FT the update is applied to matrix U, while in cases
    of GLP_BF_BG and GLP_BF_GR the update is applied to the Schur complement.

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