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Re: [Help-gsl] (in)accuracy of gsl_poly_complex_solve for repeated roots

From: Brian Gough
Subject: Re: [Help-gsl] (in)accuracy of gsl_poly_complex_solve for repeated roots?
Date: Fri, 10 Jun 2005 19:23:48 +0100

Steven G. Johnson writes:
 > Hi, I noticed that gsl_poly_complex_solve seems to be surprisingly 
 > inaccurate.  For example, if you ask it for the roots of 1 + 4x + 6x^2 + 
 > 4x^3 + x^4, which should have x = -1 as a four-fold root (note that the 
 > coefficients and solutions are exactly representable), it gives roots:

Thanks, I will add a note about it in the manual.  Higher multiplicity
roots are always more sensitive to numerical error as there is a
factor of (macheps)^(1/n) in the error for a root of multiplicity n.

Brian Gough

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