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<a name="Troubleshooting"></a>
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<p>
Next: <a href="Fitting-Examples.html#Fitting-Examples" accesskey="n" rel="next">Fitting Examples</a>, Previous: <a href="Large-Dense-Linear-Systems.html#Large-Dense-Linear-Systems" accesskey="p" rel="previous">Large Dense Linear Systems</a>, Up: <a href="Least_002dSquares-Fitting.html#Least_002dSquares-Fitting" accesskey="u" rel="up">Least-Squares Fitting</a> &nbsp; [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
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<a name="Troubleshooting-1"></a>
<h3 class="section">38.7 Troubleshooting</h3>
<a name="index-least-squares-troubleshooting"></a>

<p>When using models based on polynomials, care should be taken when constructing the design matrix
<em>X</em>. If the <em>x</em> values are large, then the matrix <em>X</em> could be ill-conditioned
since its columns are powers of <em>x</em>, leading to unstable least-squares solutions.
In this case it can often help to center and scale the <em>x</em> values using the mean and standard deviation:
</p>
<div class="example">
<pre class="example">x' = (x - mu)/sigma
</pre></div>

<p>and then construct the <em>X</em> matrix using the transformed values <em>x'</em>.
</p>



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