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From: jonathan <johnscpg@googlemail.com>
Newsgroups: comp.lang.ada
Subject: Re: matrix package with Ada
Date: Tue, 27 Jul 2010 15:10:10 -0700 (PDT)
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I found another bug in  Generic_Complex_Eigenvalues.

(From the collection at  http://www.csee.umbc.edu/~squire/adaclass/gnatmath95/).

Wherever you find   2.0**( -23)   in the code, it should be replaced
with Acc_Init, where

  Acc_Init : constant Real := Real'Epsilon * 2.0**(-3);
  -- 2**(-23) for digits 6, and 2**(-53) for digits 15, assuming usual
IEEE.

At the moment  Generic_Complex_Eigenvalues  only gives you single
precision
(digits 6), so it fails as a generic in the floating point type Real.

Also the program works poorly on matrices that are ill-conditioned,
and
it fails catastrophically on singular matrices.  There is still
a large class of problems where it may be useful, but its limitations
should be loudly stated somewhere in  .ads  file.

J.