errors/errors.html

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      ERRORS - Failures of Numerical Algorithms
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      ERRORS <br> Failures of Numerical Algorithms
    </h1>

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    <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>

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      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>

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      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>

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      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>

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      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>

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    <i>
      Last revised on 01 January 2011.
    </i>

    <!-- John Burkardt -->

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