Failures of Numerical Algorithms
is a MATLAB program which
demonstrates how reasonable computations
can produce numerical nonsense. This illustrates that the programmer
must not assume that a numerical algorithm that seems reasonable will
always produce correct and reliable results.
include polynomial evaluation and root finding, linear system solution,
minimization, and Taylor series approximation.
The computer code and data files described and made available on this
web page are distributed under
the GNU LGPL license.
ERRORS is available in
a FORTRAN90 version and
a MATLAB version.
Related Data and Programs:
U Kulisch, C Ullrich, Editors,
Wissenschaftliches Rechnen und Programmiersprachen,
(Scientific Computing and Programming Languages),
Berichte des German Chapter of the ACM,
(Reports of the German Chapter of the ACM),
Volume 10, Teubner Verlag, 1982.
Cleve Moler, Charles Van Loan,
19 Dubious Ways to Compute the Exponential of a Matrix,
25 Years Later,
Volume 45, Number 1, pages 3-49, March 2003.
Numerical Linear Algebra on the HP-28, or How to Lie with
The American Mathematical Monthly,
Volume 98, Number 6, June-July 1991, pages 539-544.
Wie Zuverlaessig Sind die Ergebnisse Unserer Rechenanlagen?
(How Reliable are the Results of our Computations?)
Jahrbuch Ueberblicke Mathematik 1983, pages 163-168.
Last revised on 10 January 2019.