File: Nonlinear-Least_002dSquares-TRS-Double-Dogleg.html

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Next: <a href="Nonlinear-Least_002dSquares-TRS-2D-Subspace.html#Nonlinear-Least_002dSquares-TRS-2D-Subspace" accesskey="n" rel="next">Nonlinear Least-Squares TRS 2D Subspace</a>, Previous: <a href="Nonlinear-Least_002dSquares-TRS-Dogleg.html#Nonlinear-Least_002dSquares-TRS-Dogleg" accesskey="p" rel="previous">Nonlinear Least-Squares TRS Dogleg</a>, Up: <a href="Nonlinear-Least_002dSquares-TRS-Overview.html#Nonlinear-Least_002dSquares-TRS-Overview" accesskey="u" rel="up">Nonlinear Least-Squares TRS Overview</a> &nbsp; [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
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<a name="Double-Dogleg"></a>
<h4 class="subsection">39.2.4 Double Dogleg</h4>
<a name="index-double-Dogleg-algorithm"></a>
<a name="index-Dogleg-algorithm_002c-double"></a>
<a name="index-nonlinear-least-squares_002c-double-dogleg"></a>

<p>This method is an improvement over the classical dogleg
algorithm, which attempts to include information about
the Gauss-Newton step while the iteration is still far from
the minimum. When the Cauchy point is inside the trust region
and the Gauss-Newton point is outside, the method computes
a scaled Gauss-Newton point and then takes a dogleg step
between the Cauchy point and the scaled Gauss-Newton point.
The scaling is calculated to ensure that the reduction
in the model <em>m_k</em> is about the same as the reduction
provided by the Cauchy point.
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