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<title>GNU Scientific Library – Reference Manual: Large Dense Linear Systems Solution Steps</title>
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<a name="Large-Dense-Linear-Systems-Solution-Steps"></a>
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<p>
Next: <a href="Large-Dense-Linear-Systems-Routines.html#Large-Dense-Linear-Systems-Routines" accesskey="n" rel="next">Large Dense Linear Systems Routines</a>, Previous: <a href="Large-Dense-Linear-Systems-TSQR.html#Large-Dense-Linear-Systems-TSQR" accesskey="p" rel="previous">Large Dense Linear Systems TSQR</a>, Up: <a href="Large-Dense-Linear-Systems.html#Large-Dense-Linear-Systems" accesskey="u" rel="up">Large Dense Linear Systems</a> [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
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<a name="Large-Dense-Linear-Systems-Solution-Steps-1"></a>
<h4 class="subsection">38.6.3 Large Dense Linear Systems Solution Steps</h4>
<a name="index-large-linear-least-squares_002c-steps"></a>
<p>The typical steps required to solve large regularized linear least
squares problems are as follows:
</p>
<ol>
<li> Choose the regularization matrix <em>L</em>.
</li><li> Construct a block of rows of the least squares matrix, right
hand side vector, and weight vector (<em>X_i</em>, <em>y_i</em>, <em>w_i</em>).
</li><li> Transform the block to standard form (<em>\tilde{X_i}</em>,<em>\tilde{y_i}</em>). This
step can be skipped if <em>L = I</em> and <em>W = I</em>.
</li><li> Accumulate the standard form block (<em>\tilde{X_i}</em>,<em>\tilde{y_i}</em>) into
the system.
</li><li> Repeat steps 2-4 until the entire matrix and right hand side vector have
been accumulated.
</li><li> Determine an appropriate regularization parameter <em>\lambda</em> (using for example
L-curve analysis).
</li><li> Solve the standard form system using the chosen <em>\lambda</em>.
</li><li> Backtransform the standard form solution <em>\tilde{c}</em> to recover the
original solution vector <em>c</em>.
</li></ol>
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