ERRORS
Failures of Numerical Algorithms

ERRORS 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.

The computations include polynomial evaluation and root finding, linear system solution, minimization, and Taylor series approximation.

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Languages:

ERRORS is available in a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

errors_test

Reference:

1. 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.
2. Cleve Moler, Charles Van Loan,
   19 Dubious Ways to Compute the Exponential of a Matrix, 25 Years Later, SIAM Review,
   Volume 45, Number 1, pages 3-49, March 2003.
3. Yves Nievergelt,
   Numerical Linear Algebra on the HP-28, or How to Lie with Supercalculators,
   The American Mathematical Monthly,
   Volume 98, Number 6, June-July 1991, pages 539-544.
4. Siegfried Rump,
   Wie Zuverlaessig Sind die Ergebnisse Unserer Rechenanlagen?
   (How Reliable are the Results of our Computations?)
   Jahrbuch Ueberblicke Mathematik 1983, pages 163-168.

Source Code:

• errors_test01.m
• errors_test02.m
• errors_test03.m
• errors_test04.m
• errors_test05.m
• errors_test06.m
• errors_test065.m
• errors_test07.m
• errors_test08.m
• errors_test09.m
• errors_test10.m
• errors_test11.m
• errors_test12.m
• errors_test13.m
• errors_test14.m
• errors_test15.m
• errors_test16.m
• errors_test17.m
• errors_test18.m
• errors_test19.m
• errors_test20.m
• errors_test21.m
• errors_test22.m
• errors_test23.m
• errors_test24.m
• errors_test26.m
• errors_test27.m
• f8.m evaluates a certain polynomial using Horner's method.
• f11.m evaluates a certain polynomial using Horner's method.
• fx15.m evaluates a certain function.
• i4_lcm_12n.m returns the lowest common multiple of integers 1 to N.
• r8mat_expm1.m evaluates the matrix exponential function.
• r8mat_expm2.m evaluates the matrix exponential function.
• r8mat_expm3.m evaluates the matrix exponential function.
• r8mat_print.m, prints an R8MAT;
• r8mat_print_some.m, prints some of an R8MAT;
• r8poly_value.m, evaluates a polynomial using a naive method;
• r8poly_value_horner.m, evaluates a polynomial using Horner's method;
• r8poly2_roots_alternate.m, returns the two roots of a quadratic polynomial.
• r8poly2_roots_standard.m, returns the two roots of a quadratic polynomial.
• r8vec_print.m, prints an R8VEC;
• r8vec3_print.m, prints an R8VEC3;
• timestamp.m, prints the YMDHMS date as a timestamp.