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Re: [Help-gsl] bug in gsl_linalg_LU_invert?

From: Jordi Gutiérrez Hermoso
Subject: Re: [Help-gsl] bug in gsl_linalg_LU_invert?
Date: Thu, 1 May 2008 17:09:53 -0500

On 28/04/2008, address@hidden <address@hidden> wrote:
>  I've checked that the det(sigma) > 0.

Oh, btw: determinants are a very poor method to gauge the numerical
invertibility of a matrix. Consider, a 0.1*Id, where Id is the 100x100
identity matrix. The determinant of that matrix would be very small,
whereas its condition number is 1. On the other hand, consider Id - U
where U is a strictly upper triangular matrix of ones (zeroes along
the diagonal too). Then if Id - U is 100x100, its condition number is
100*2^99 (and if you try to invert it, you'll see that entries get
exponentially large).

These examples are from section 2.7.3 of Golub and Van Loan.

My guess is still that you're attempting to invert an ill-conditioned
matrix, so please show us your matrix.

- Jordi G. H.

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