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<a name="mnewton"></a>
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<h1 class="chapter"> 64. mnewton </h1>

<table class="menu" border="0" cellspacing="0">
<tr><td align="left" valign="top"><a href="#SEC266">64.1 Introduction to mnewton</a></td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top"><a href="#SEC267">64.2 Functions and Variables for mnewton</a></td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
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<p><a name="Item_003a-Introduction-to-mnewton"></a>
</p><hr size="6">
<a name="Introduction-to-mnewton"></a>
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<h2 class="section"> 64.1 Introduction to mnewton </h2>

<p><code>mnewton</code> is an implementation of Newton's method for solving nonlinear equations
in one or more variables.
</p>
<div class=categorybox>


<p>Categories:&nbsp;&nbsp;<a href="maxima_95.html#Category_003a-Numerical-methods">Numerical methods</a>
 &middot;
<a href="maxima_95.html#Category_003a-Share-packages">Share packages</a>
 &middot;
<a href="maxima_95.html#Category_003a-Package-mnewton">Package mnewton</a>
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<p><a name="Item_003a-Functions-and-Variables-for-mnewton"></a>
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<h2 class="section"> 64.2 Functions and Variables for mnewton </h2>

<p><a name="Item_003a-newtonepsilon"></a>
</p><dl>
<dt><u>Option variable:</u> <b>newtonepsilon</b>
<a name="IDX2371"></a>
</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>See also <code>mnewton</code>.
</p>
<div class=categorybox>


<p>Categories:&nbsp;&nbsp;<a href="maxima_95.html#Category_003a-Package-mnewton">Package mnewton</a>
</p>
</div>


</dd></dl>


<p><a name="Item_003a-newtonmaxiter"></a>
</p><dl>
<dt><u>Option variable:</u> <b>newtonmaxiter</b>
<a name="IDX2372"></a>
</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>mnewton</code>.
</p>
<div class=categorybox>


<p>Categories:&nbsp;&nbsp;<a href="maxima_95.html#Category_003a-Package-mnewton">Package mnewton</a>
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</div>


</dd></dl>



<dl>
<dt><u>Function:</u> <b>mnewton</b><i> (<var>FuncList</var>,<var>VarList</var>,<var>GuessList</var>)</i>
<a name="IDX2373"></a>
</dt>
<dd><p>Multiple nonlinear functions solution using the Newton method.
<var>FuncList</var> is the list of functions to solve,
<var>VarList</var> is the list of variable names, and
<var>GuessList</var> is the list of initial approximations.
</p>
<p>The solution is returned in the same format that <code>solve()</code> returns.
If the solution isn't found, <code>[]</code> is returned.
</p>
<p>This function is controlled by global variables <code>newtonepsilon</code> and <code>newtonmaxiter</code>.
</p>
<pre class="example">(%i1) load(&quot;mnewton&quot;)$

(%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>
<p>To use this function write first <code>load(&quot;mnewton&quot;)</code>. See also <code>newtonepsilon</code> and <code>newtonmaxiter</code>.
</p>
<div class=categorybox>


<p>Categories:&nbsp;&nbsp;<a href="maxima_95.html#Category_003a-Package-mnewton">Package mnewton</a>
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