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<html>
<head>
<title>
ERRORS - Failures of Numerical Algorithms
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
ERRORS <br> Failures of Numerical Algorithms
</h1>
<hr>
<p>
<b>ERRORS</b>
is a FORTRAN90 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.
</p>
<p>
The computations
include polynomial evaluation and root finding, linear system solution,
minimization, and Taylor series approximation.
</p>
<h3 align = "center">
Licensing:
</h3>
<p>
The computer code and data files described and made available on this
web page are distributed under
<a href = "../../txt/gnu_lgpl.txt">the GNU LGPL license.</a>
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
U Kulisch, C Ullrich, Editors,<br>
Wissenschaftliches Rechnen und Programmiersprachen,<br>
(Scientific Computing and Programming Languages),<br>
Berichte des German Chapter of the ACM,<br>
(Reports of the German Chapter of the ACM),<br>
Volume 10, Teubner Verlag, 1982.
</li>
<li>
Cleve Moler, Charles Van Loan,<br>
19 Dubious Ways to Compute the Exponential of a Matrix,
25 Years Later,
SIAM Review, <br>
Volume 45, Number 1, pages 3-49, March 2003.
</li>
<li>
Yves Nievergelt,<br>
Numerical Linear Algebra on the HP-28, or How to Lie with
Supercalculators,<br>
The American Mathematical Monthly,<br>
Volume 98, Number 6, June-July 1991, pages 539-544.
</li>
<li>
Siegfried Rump,<br>
Wie Zuverlaessig Sind die Ergebnisse Unserer Rechenanlagen?<br>
(How Reliable are the Results of our Computations?)<br>
Jahrbuch Ueberblicke Mathematik 1983, pages 163-168.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "errors.f90">errors.f90</a>, the source code;
</li>
<li>
<a href = "errors.sh">errors.sh</a>,
commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "errors_prb.f90">errors_prb.f90</a>, the calling program;
</li>
<li>
<a href = "errors_prb.sh">errors_prb.sh</a>,
commands to compile, link and run the calling program;
</li>
<li>
<a href = "errors_prb_output.txt">errors_prb_output.txt</a>,
the output file.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>DPOLY_VAL</b> evaluates a double precision polynomial.
</li>
<li>
<b>DPOLY_VAL_HORNER</b> evaluates a double precision polynomial using Horner's method.
</li>
<li>
<b>DPOLY2_ROOTS</b> finds the roots of a quadratic polynomial.
</li>
<li>
<b>DPOLY2_ROOTS2</b> finds the roots of a quadratic polynomial.
</li>
<li>
<b>FMIN</b> seeks a minimizer of a scalar function of a scalar variable.
</li>
<li>
<b>ISAMAX</b> finds the index of the vector element of maximum absolute value.
</li>
<li>
<b>LCM_12N</b> computes the least common multiple of the integers 1 through N.
</li>
<li>
<b>MAXTRIX_EXPONENTIAL_TAYLOR</b> uses a Taylor series for the matrix exponential.
</li>
<li>
<b>RPOLY_VAL</b> evaluates a real polynomial.
</li>
<li>
<b>RPOLY_VAL_HORNER</b> evaluates a real polynomial using Horner's method.
</li>
<li>
<b>RPOLY2_ROOTS</b> finds the roots of a quadratic polynomial.
</li>
<li>
<b>RPOLY2_ROOTS2</b> finds the roots of a quadratic polynomial.
</li>
<li>
<b>SAMAX</b> returns the maximum absolute value of the entries in a vector.
</li>
<li>
<b>SAXPY</b> adds a constant times one vector to another.
</li>
<li>
<b>SCOPY</b> copies one real vector into another.
</li>
<li>
<b>SDOT</b> forms the dot product of two vectors.
</li>
<li>
<b>SDSDOT</b> forms the dot product of two vectors using higher precision.
</li>
<li>
<b>SGEDI</b> computes the determinant and inverse of a matrix factored by SGECO or SGEFA.
</li>
<li>
<b>SGEFA</b> factors a real matrix.
</li>
<li>
<b>SGESL</b> solves a real general linear system A * X = B.
</li>
<li>
<b>RVEC_NORM2</b> computes the Euclidean norm of a vector.
</li>
<li>
<b>SQRDC</b> computes the QR factorization of a real rectangular matrix.
</li>
<li>
<b>SQRSL</b> computes transformations, projections, and least squares solutions.
</li>
<li>
<b>SSCAL</b> scales a vector by a constant.
</li>
<li>
<b>SSWAP</b> interchanges two vectors.
</li>
<li>
<b>TIMESTAMP</b> prints the current YMDHMS date as a time stamp.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../f_src.html">
the FORTRAN90 source codes</a>.
</p>
<hr>
<i>
Last revised on 01 January 2011.
</i>
<!-- John Burkardt -->
</body>
</html>