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<a name="Residual-optimization"></a>
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<p>
Next: <a href="Zero-finders.html#Zero-finders" accesskey="n" rel="next">Zero finders</a>, Previous: <a href="Scalar-optimization.html#Scalar-optimization" accesskey="p" rel="prev">Scalar optimization</a>, Up: <a href="index.html#Top" accesskey="u" rel="up">Top</a> [<a href="Function-index.html#Function-index" title="Index" rel="index">Index</a>]</p>
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<hr>
<a name="Functions-for-optimization-of-a-model-function-returning-an-array"></a>
<h2 class="chapter">2 Functions for optimization of a model function returning an array</h2>
<a name="index-residual-optimization"></a>
<p>Model functions whose parameters are to be optimized may return a vector
or array of values. Either these or their differences to some constant
values (curve fitting) can be minimized in some sense, often, but not
necessarily, by minimizing the sum of their squares. It is usually
preferable to use optimizers designed for residual optimization for this
purpose. These can exploit information contained in the individual
elements of the returned array, which would not be possible if the user
calculated a norm (<abbr>e.g.</abbr> sum of squares) of the elements and
performed a scalar optimization.
</p>
<table class="menu" border="0" cellspacing="0">
<tr><th colspan="3" align="left" valign="top"><pre class="menu-comment">Optimization frontends
</pre></th></tr><tr><td align="left" valign="top">• <a href="nonlin_005fresidmin.html#nonlin_005fresidmin" accesskey="1">nonlin_residmin</a>:</td><td> </td><td align="left" valign="top">The standard interface for non-linear
residual minimization.
</td></tr>
<tr><td align="left" valign="top">• <a href="nonlin_005fcurvefit.html#nonlin_005fcurvefit" accesskey="2">nonlin_curvefit</a>:</td><td> </td><td align="left" valign="top">A convenience interface, curve fitting.
</td></tr>
<tr><th colspan="3" align="left" valign="top"><pre class="menu-comment">
Optimization backends
</pre></th></tr><tr><td align="left" valign="top">• <a href="lm_005fsvd_005ffeasible.html#lm_005fsvd_005ffeasible" accesskey="3">lm_svd_feasible</a>:</td><td> </td><td align="left" valign="top">L/M algorithm with SVD, constraints met
throughout optimization.
</td></tr>
<tr><th colspan="3" align="left" valign="top"><pre class="menu-comment">
Statistics frontends
</pre></th></tr><tr><td align="left" valign="top">• <a href="residmin_005fstat.html#residmin_005fstat" accesskey="4">residmin_stat</a>:</td><td> </td><td align="left" valign="top">Statistics for residual minimization.
</td></tr>
<tr><td align="left" valign="top">• <a href="curvefit_005fstat.html#curvefit_005fstat" accesskey="5">curvefit_stat</a>:</td><td> </td><td align="left" valign="top">Statistics for curve fitting.
</td></tr>
<tr><th colspan="3" align="left" valign="top"><pre class="menu-comment">
Statistics backends
</pre></th></tr><tr><td align="left" valign="top">• <a href="wls.html#wls" accesskey="6">wls</a>:</td><td> </td><td align="left" valign="top">Statistics for weighted least squares.
</td></tr>
<tr><th colspan="3" align="left" valign="top"><pre class="menu-comment">
Standalone functions
</pre></th></tr><tr><td align="left" valign="top">• <a href="lsqlin.html#lsqlin" accesskey="7">lsqlin</a>:</td><td> </td><td align="left" valign="top">Linear least squares with linear
constraints.
</td></tr>
<tr><td align="left" valign="top">• <a href="leasqr.html#leasqr" accesskey="8">leasqr</a>:</td><td> </td><td align="left" valign="top">An older function for curve fitting.
</td></tr>
<tr><td align="left" valign="top">• <a href="pronyfit.html#pronyfit" accesskey="9">pronyfit</a>:</td><td> </td><td align="left" valign="top">Prony’s method for non-linear exponential
fitting.
</td></tr>
<tr><td align="left" valign="top">• <a href="polyfitinf.html#polyfitinf">polyfitinf</a>:</td><td> </td><td align="left" valign="top">Function polyfitinf for polynomial
fitting.
</td></tr>
<tr><td align="left" valign="top">• <a href="wpolyfit.html#wpolyfit">wpolyfit</a>:</td><td> </td><td align="left" valign="top">Polynomial fitting suitable for polyconf.
</td></tr>
<tr><td align="left" valign="top">• <a href="polyconf.html#polyconf">polyconf</a>:</td><td> </td><td align="left" valign="top">Confidence and prediction intervals for
polynomial fitting.
</td></tr>
<tr><td align="left" valign="top">• <a href="LinearRegression.html#LinearRegression">LinearRegression</a>:</td><td> </td><td align="left" valign="top">Function LinearRegression.
</td></tr>
<tr><td align="left" valign="top">• <a href="wsolve.html#wsolve">wsolve</a>:</td><td> </td><td align="left" valign="top">Another linear solver.
</td></tr>
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Next: <a href="Zero-finders.html#Zero-finders" accesskey="n" rel="next">Zero finders</a>, Previous: <a href="Scalar-optimization.html#Scalar-optimization" accesskey="p" rel="prev">Scalar optimization</a>, Up: <a href="index.html#Top" accesskey="u" rel="up">Top</a> [<a href="Function-index.html#Function-index" title="Index" rel="index">Index</a>]</p>
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