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Previous: <a href="Fitting-Examples.html#Fitting-Examples" accesskey="p" rel="previous">Fitting Examples</a>, Up: <a href="Least_002dSquares-Fitting.html#Least_002dSquares-Fitting" accesskey="u" rel="up">Least-Squares Fitting</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-30"></a>
<h3 class="section">38.9 References and Further Reading</h3>
<p>A summary of formulas and techniques for least squares fitting can be
found in the “Statistics” chapter of the Annual Review of Particle
Physics prepared by the Particle Data Group,
</p>
<ul class="no-bullet">
<li><!-- /@w --> <cite>Review of Particle Properties</cite>,
R.M. Barnett et al., Physical Review D54, 1 (1996)
<a href="http://pdg.lbl.gov/">http://pdg.lbl.gov/</a>
</li></ul>
<p>The Review of Particle Physics is available online at the website given
above.
</p>
<a name="index-NIST-Statistical-Reference-Datasets"></a>
<a name="index-Statistical-Reference-Datasets-_0028StRD_0029"></a>
<p>The tests used to prepare these routines are based on the NIST
Statistical Reference Datasets. The datasets and their documentation are
available from NIST at the following website,
</p>
<div align="center"><a href="http://www.nist.gov/itl/div898/strd/index.html">http://www.nist.gov/itl/div898/strd/index.html</a>.
</div>
<p>More information on Tikhonov regularization can be found in
</p>
<ul class="no-bullet">
<li><!-- /@w --> Hansen, P. C. (1998), Rank-Deficient and Discrete Ill-Posed Problems:
Numerical Aspects of Linear Inversion. SIAM Monogr. on Mathematical
Modeling and Computation, Society for Industrial and Applied Mathematics
</li><li><!-- /@w --> M. Rezghi and S. M. Hosseini (2009), A new variant of L-curve for
Tikhonov regularization, Journal of Computational and Applied Mathematics,
Volume 231, Issue 2, pages 914-924.
</li></ul>
<p>The GSL implementation of robust linear regression closely follows the publications
</p>
<ul class="no-bullet">
<li><!-- /@w --> DuMouchel, W. and F. O’Brien (1989), "Integrating a robust
option into a multiple regression computing environment,"
Computer Science and Statistics: Proceedings of the 21st
Symposium on the Interface, American Statistical Association
</li><li><!-- /@w --> Street, J.O., R.J. Carroll, and D. Ruppert (1988), "A note on
computing robust regression estimates via iteratively
reweighted least squares," The American Statistician, v. 42,
pp. 152-154.
</li></ul>
<p>More information about the normal equations and TSQR approach for solving
large linear least squares systems can be found in the publications
</p>
<ul class="no-bullet">
<li><!-- /@w --> Trefethen, L. N. and Bau, D. (1997), "Numerical Linear Algebra", SIAM.
</li><li><!-- /@w --> Demmel, J., Grigori, L., Hoemmen, M. F., and Langou, J.
"Communication-optimal parallel and sequential QR and LU factorizations",
UCB Technical Report No. UCB/EECS-2008-89, 2008.
</li></ul>
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