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<a name="Functions-and-Variables-for-mnewton"></a>
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Previous: <a href="maxima_319.html#Introduction-to-mnewton" accesskey="p" rel="previous">Introduction to mnewton</a>, Up: <a href="maxima_318.html#mnewton_002dpkg" accesskey="u" rel="up">mnewton-pkg</a> [<a href="maxima_toc.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="maxima_423.html#Function-and-Variable-Index" title="Index" rel="index">Index</a>]</p>
</div>
<a name="Functions-and-Variables-for-mnewton-1"></a>
<h3 class="section">75.2 Functions and Variables for mnewton</h3>
<a name="newtonepsilon"></a><a name="Item_003a-mnewton_002fdefvr_002fnewtonepsilon"></a><dl>
<dt><a name="index-newtonepsilon"></a>Option variable: <strong>newtonepsilon</strong></dt>
<dd><p>Default value: <code>10.0^(-fpprec/2)</code>
</p>
<p>Precision to determine when the <code>mnewton</code> function has converged towards
the solution.
</p>
<p>When <code>newtonepsilon</code> is a bigfloat,
<code>mnewton</code> computations are done with bigfloats;
otherwise, ordinary floats are used.
</p>
<p>See also <code><a href="#mnewton">mnewton</a></code>.
</p>
<div class=categorybox>
Categories:<a href="maxima_424.html#Category_003a-Package-mnewton">Package mnewton</a>
·</div></dd></dl>
<a name="newtonmaxiter"></a><a name="Item_003a-mnewton_002fdefvr_002fnewtonmaxiter"></a><dl>
<dt><a name="index-newtonmaxiter"></a>Option variable: <strong>newtonmaxiter</strong></dt>
<dd><p>Default value: <code>50</code>
</p>
<p>Maximum number of iterations to stop the <code>mnewton</code> function
if it does not converge or if it converges too slowly.
</p>
<p>See also <code><a href="#mnewton">mnewton</a></code>.
</p>
<div class=categorybox>
Categories:<a href="maxima_424.html#Category_003a-Package-mnewton">Package mnewton</a>
·</div></dd></dl>
<a name="newtondebug"></a><a name="Item_003a-mnewton_002fdefvr_002fnewtondebug"></a><dl>
<dt><a name="index-newtondebug"></a>Option variable: <strong>newtondebug</strong></dt>
<dd><p>Default value: <code>false</code>
</p>
<p>When <code>newtondebug</code> is <code>true</code>,
<code>mnewton</code> prints out debugging information while solving a problem.
</p>
<div class=categorybox>
Categories:<a href="maxima_424.html#Category_003a-Package-mnewton">Package mnewton</a>
·</div></dd></dl>
<a name="mnewton"></a><a name="Item_003a-mnewton_002fdeffn_002fmnewton"></a><dl>
<dt><a name="index-mnewton"></a>Function: <strong>mnewton</strong> <em><br> <tt>mnewton</tt> (<var>FuncList</var>, <var>VarList</var>, <var>GuessList</var>) <br> <tt>mnewton</tt> (<var>FuncList</var>, <var>VarList</var>, <var>GuessList</var>, <var>DF</var>)</em></dt>
<dd>
<p>Approximate solution of multiple nonlinear equations by Newton’s method.
</p>
<p><var>FuncList</var> is a list of functions to solve,
<var>VarList</var> is a list of variable names, and
<var>GuessList</var> is a list of initial approximations.
The optional argument <var>DF</var> is the Jacobian matrix of the list of functions;
if not supplied, it is calculated automatically from <var>FuncList</var>.
</p>
<p><var>FuncList</var> may be specified as a list of equations,
in which case the function to be solved is the left-hand side of each equation minus the right-hand side.
</p>
<p>If there is only a single function, variable, and initial point,
they may be specified as a single expression, variable, and initial value;
they need not be lists of one element.
</p>
<p>A variable may be a simple symbol or a subscripted symbol.
</p>
<p>The solution, if any, is returned as a list of one element,
which is a list of equations, one for each variable,
specifying an approximate solution;
this is the same format as returned by <code>solve</code>.
If the solution is not found, <code>[]</code> is returned.
</p>
<p>Functions and initial points may contain complex numbers,
and solutions likewise may contain complex numbers.
</p>
<p><code>mnewton</code> is governed by global variables <code><a href="#newtonepsilon">newtonepsilon</a></code> and
<code><a href="#newtonmaxiter">newtonmaxiter</a></code>, and the global flag <code><a href="#newtondebug">newtondebug</a></code>.
</p>
<p><code>load("mnewton")</code> loads this function.
</p>
<p>See also <code><a href="maxima_108.html#realroots">realroots</a></code>, <code><a href="maxima_108.html#allroots">allroots</a></code>, <code><a href="maxima_116.html#find_005froot">find_root</a></code> and
<code><a href="maxima_116.html#newton">newton</a></code>.
</p>
<p>Examples:
</p>
<div class="example">
<pre class="example">(%i1) load("mnewton")$
(%i2) mnewton([x1+3*log(x1)-x2^2, 2*x1^2-x1*x2-5*x1+1],
[x1, x2], [5, 5]);
(%o2) [[x1 = 3.756834008012769, x2 = 2.779849592817897]]
(%i3) mnewton([2*a^a-5],[a],[1]);
(%o3) [[a = 1.70927556786144]]
(%i4) mnewton([2*3^u-v/u-5, u+2^v-4], [u, v], [2, 2]);
(%o4) [[u = 1.066618389595407, v = 1.552564766841786]]
</pre></div>
<p>The variable <code>newtonepsilon</code> controls the precision of the
approximations. It also controls if computations are performed with
floats or bigfloats.
</p>
<div class="example">
<pre class="example">(%i1) load("mnewton")$
(%i2) (fpprec : 25, newtonepsilon : bfloat(10^(-fpprec+5)))$
(%i3) mnewton([2*3^u-v/u-5, u+2^v-4], [u, v], [2, 2]);
(%o3) [[u = 1.066618389595406772591173b0,
v = 1.552564766841786450100418b0]]
</pre></div>
<div class=categorybox>
Categories:<a href="maxima_424.html#Category_003a-Package-mnewton">Package mnewton</a>
·</div></dd></dl>
<hr>
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Previous: <a href="maxima_319.html#Introduction-to-mnewton" accesskey="p" rel="previous">Introduction to mnewton</a>, Up: <a href="maxima_318.html#mnewton_002dpkg" accesskey="u" rel="up">mnewton-pkg</a> [<a href="maxima_toc.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="maxima_423.html#Function-and-Variable-Index" title="Index" rel="index">Index</a>]</p>
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