URL:
<http://savannah.gnu.org/bugs/?43496>
Summary: Possible error in brent minimizer convergence
criteria
Project: GNU Scientific Library
Submitted by: psa
Submitted on: Wed 29 Oct 2014 02:16:09 PM GMT
Category: Runtime error
Severity: 3 - Normal
Operating System:
Status: None
Assigned to: None
Open/Closed: Open
Release:
Discussion Lock: Any
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Details:
In GSL, min/brent.c:128 has this for the evaluation of the parabolic fit:
if (fabs (p) < fabs (0.5 * q * r) && p < q * w_lower && p < q * w_upper)
This matches the Algol60 implementation given by Richard Brent in the book.
Unfortunately, there seems to be a transcription (or similar) error and the
code should actually be
if (fabs (p) < fabs (0.5 * q * r) && p > q * w_lower && p < q * w_upper)
which matches the actual text of the book which says that the algorithm takes
the golden section path under some conditions, including “x+p/q not in
(a,b)” which would translate to:
x + p/q <= a || x +p/q >= b …
p <= q * (a - x) || p >= q * (b - x) …
p > q * (a - x) && p < q * (b - x)
In fact, other authors such as Forsythe have found and corrected the error.
Netlib implementation of fmin.f is also corrected (seems to be the same as
that in the Forsythe book). The Numerical Recipes and boost implementations
are also fixed.
Some references for further information:
· http://www.netlib.org/go/fmin.f
· http://www.nr.com/forum/showthread.php?p=4893
· Computer Methods for Mathematical Computations – G.E. Forsythe,
Michael A. Malcolm, Cleve B. Moler. Prentice Hall. ISBN 0-13-165332-6.
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