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## Re: [Help-glpk] Precison Question?

 From: glpk xypron Subject: Re: [Help-glpk] Precison Question? Date: Thu, 29 Jul 2010 00:14:52 +0200

```Hello Steven,

GLPK provides an implementation of the simplex algorithm
using rational numbers. For speedup the
GNU MP bignum library can be used.

See the documention of function glp_exact() in
glpk-4.44/doc/glpk.pdf

The source of GLPK is available at
ftp://ftp.gnu.org/gnu/glpk/glpk-4.44.tar.gz

http://www.cise.ufl.edu/~davis/Morgan/
gives an overview of different implementations of the
simplex algorithm, pointing out that accuracy can be increased
by using the Bartels-Golub method.

GLPK provides different factorization methods as described in the
documentation of function glp_set_bfcp().

Best regards

Xypron

-------- Original-Nachricht --------
> Datum: Wed, 28 Jul 2010 15:25:12 +0800
> Betreff: [Help-glpk] Precison Question?

> Hello, I have implemented a solver using two-staged simplex method.
> And the element type of coefficient matrix can be double and rational,
> e.g:
>       the rational version:
>               //lineq is a (2*3) matrix.
>               MATRIX<RATIONAL> lineq( //means linear inequalities
>                       3, 2, 6  //means 3x1 + 3x2 <= 6
>                       -3, 2, 0  //means -3x1 + 2x2 <= 0
>
>               );
>               max: x1 + x2
>
>       the double version:
>               MATRIX<double> lineq(
>                       3.0, 2.0, 6.0  //means 3.0x1 + 2.0x2 <= 6.0
>                       -3.0, 2.0, 0.0
>               );
>               max: x1 + x2
>
> The solver works well when the element type of 'lineq' was rational.
> But If the element type is double, there are always cumulative error
> when 'lineq' was growing up to (500*700) or more,
> and that incurring to that the result is unbound.
> So my question is how did you handle the cumulative error in GLPK?
>