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## Re: [Help-gsl] Mistake in the documentation ?

**From**: |
kamaraju kusumanchi |

**Subject**: |
Re: [Help-gsl] Mistake in the documentation ? |

**Date**: |
Thu, 23 Jul 2009 12:19:49 -0400 |

2009/7/22 Maxime Boissonneault <address@hidden>:
>* Hello,*
>* I am reading the documentation to do multidimensionnal minimization with*
>* GSL. I think there is a mistake on that page :*
>* http://www.gnu.org/software/gsl/manual/html_node/Multimin-Algorithms-without-Derivatives.html*
>
>* It says "They construct n vectors p_i from the starting vector x and the*
>* vector step_size as follows..." According to the following, it should be*
>* "They construct n+1 vectors p_i from the..."*
>
>* Can someone who understand the algorithm better confirm ?*
>
To form an n-dimensional simplex you need n+1 vectors. The initial
vector is p_0. The algorithm constructs an "additional" n vectors. I
agree that there is an ambiguity in the documentation. Also, the
subscript to step_size (in the formulas) is a bit confusing. Usually
when writing subscripts, the vector names are just a single letter.
(we write x_i not zyx_i )
The improved construction could be
Starting from the initial vector p_0, the algorithm constructs an
additional n vectors p_i (i=1 through n) using the step size vector s
as follows
p_0 = (x_0, x_1, ..., x_n)
p_1 = (x_0 + s_0, x_1, ..., x_n)
p_2 = (x_0, x_1 + s_1, ..., x_n)
... = ...
p_n = (x_0, x_1, ..., x_n + s_n)
What do you guys think? If necessary, I can submit a patch for this.
raju