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Previous: <a href="Linear-Algebra-Examples.html#Linear-Algebra-Examples" accesskey="p" rel="previous">Linear Algebra Examples</a>, Up: <a href="Linear-Algebra.html#Linear-Algebra" accesskey="u" rel="up">Linear Algebra</a> [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
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<a name="References-and-Further-Reading-8"></a>
<h3 class="section">14.21 References and Further Reading</h3>
<p>Further information on the algorithms described in this section can be
found in the following book,
</p>
<ul class="no-bullet">
<li><!-- /@w --> G. H. Golub, C. F. Van Loan, <cite>Matrix Computations</cite> (3rd Ed, 1996),
Johns Hopkins University Press, ISBN 0-8018-5414-8.
</li></ul>
<p>The <small>LAPACK</small> library is described in the following manual,
</p>
<ul class="no-bullet">
<li><!-- /@w --> <cite>LAPACK Users’ Guide</cite> (Third Edition, 1999), Published by SIAM,
ISBN 0-89871-447-8.
<p><a href="http://www.netlib.org/lapack">http://www.netlib.org/lapack</a>
</p></li></ul>
<p>The <small>LAPACK</small> source code can be found at the website above, along
with an online copy of the users guide.
</p>
<p>The Modified Golub-Reinsch algorithm is described in the following paper,
</p>
<ul class="no-bullet">
<li><!-- /@w --> T.F. Chan, “An Improved Algorithm for Computing the Singular Value
Decomposition”, <cite>ACM Transactions on Mathematical Software</cite>, 8
(1982), pp 72–83.
</li></ul>
<p>The Jacobi algorithm for singular value decomposition is described in
the following papers,
</p>
<ul class="no-bullet">
<li><!-- /@w --> J.C. Nash, “A one-sided transformation method for the singular value
decomposition and algebraic eigenproblem”, <cite>Computer Journal</cite>,
Volume 18, Number 1 (1975), p 74–76
</li><li><!-- /@w --> J.C. Nash and S. Shlien “Simple algorithms for the partial singular
value decomposition”, <cite>Computer Journal</cite>, Volume 30 (1987), p
268–275.
</li><li><!-- /@w --> James Demmel, Krešimir Veselić, “Jacobi’s Method is more accurate than
QR”, <cite>Lapack Working Note 15</cite> (LAWN-15), October 1989. Available
from netlib, <a href="http://www.netlib.org/lapack/">http://www.netlib.org/lapack/</a> in the <code>lawns</code> or
<code>lawnspdf</code> directories.
</li></ul>
<p>The algorithm for estimating a matrix condition number is described in
the following paper,
</p>
<ul class="no-bullet">
<li><!-- /@w --> N. J. Higham, "FORTRAN codes for estimating the one-norm of
a real or complex matrix, with applications to condition estimation",
ACM Trans. Math. Soft., vol. 14, no. 4, pp. 381-396, December 1988.
</li></ul>
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