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Previous: <a href="Roots-of-Polynomials-Examples.html#Roots-of-Polynomials-Examples" accesskey="p" rel="previous">Roots of Polynomials Examples</a>, Up: <a href="Polynomials.html#Polynomials" accesskey="u" rel="up">Polynomials</a> &nbsp; [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
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<a name="References-and-Further-Reading-1"></a>
<h3 class="section">6.7 References and Further Reading</h3>

<p>The balanced-QR method and its error analysis are described in the
following papers,
</p>
<ul class="no-bullet">
<li><!-- /@w --> R.S. Martin, G. Peters and J.H. Wilkinson, &ldquo;The QR Algorithm for Real
Hessenberg Matrices&rdquo;, <cite>Numerische Mathematik</cite>, 14 (1970), 219&ndash;231.

</li><li><!-- /@w --> B.N. Parlett and C. Reinsch, &ldquo;Balancing a Matrix for Calculation of
Eigenvalues and Eigenvectors&rdquo;, <cite>Numerische Mathematik</cite>, 13 (1969),
293&ndash;304.

</li><li><!-- /@w --> A. Edelman and H. Murakami, &ldquo;Polynomial roots from companion matrix
eigenvalues&rdquo;, <cite>Mathematics of Computation</cite>, Vol. 64, No. 210
(1995), 763&ndash;776.
</li></ul>

<p>The formulas for divided differences are given in the following texts,
</p>
<ul class="no-bullet">
<li><!-- /@w --> Abramowitz and Stegun, <cite>Handbook of Mathematical Functions</cite>,
Sections 25.1.4 and 25.2.26.

</li><li><!-- /@w --> R. L. Burden and J. D. Faires, <cite>Numerical Analysis</cite>, 9th edition,
ISBN 0-538-73351-9, 2011.
</li></ul>




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