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@@ -1,10 +1,10 @@
<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
<title>Finding Zeros of Airy Functions</title>
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@@ -65,7 +65,7 @@
<span class="identifier">OutputIterator</span> <span class="identifier">out_it</span><span class="special">);</span> <span class="comment">// Destination for zeros.</span>
</pre>
<p>
There are also versions which allow control of the <a class="link" href="../../policy.html" title="Chapter&#160;18.&#160;Policies: Controlling Precision, Error Handling etc">Policies</a>
There are also versions which allow control of the <a class="link" href="../../policy.html" title="Chapter 21. Policies: Controlling Precision, Error Handling etc">Policies</a>
for error handling and precision.
</p>
<pre class="programlisting"> <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
@@ -102,12 +102,12 @@
real axis. The real zeros on the negative real axis can be found by solving
for the roots of
</p>
<p>
&#8193; <span class="emphasis"><em>Ai(x<sub>m</sub>) = 0</em></span>
</p>
<p>
&#8193; <span class="emphasis"><em>Bi(y<sub>m</sub>) = 0</em></span>
</p>
<div class="blockquote"><blockquote class="blockquote"><p>
<span class="emphasis"><em>Ai(x<sub>m</sub>) = 0</em></span>
</p></blockquote></div>
<div class="blockquote"><blockquote class="blockquote"><p>
<span class="emphasis"><em>Bi(y<sub>m</sub>) = 0</em></span>
</p></blockquote></div>
<p>
Here, <span class="emphasis"><em>x<sub>m</sub></em></span> represents the <span class="emphasis"><em>m<sup>th</sup></em></span> root
of the Airy Ai function, and <span class="emphasis"><em>y<sub>m</sub></em></span> represents the <span class="emphasis"><em>m<sup>th</sup></em></span>
@@ -265,9 +265,10 @@
</tr>
</tbody>
</table></div>
<p>
<span class="inlinemediaobject"><img src="../../../graphs/airy_zeros.svg" align="middle"></span>
</p>
<div class="blockquote"><blockquote class="blockquote"><p>
<span class="inlinemediaobject"><img src="../../../graphs/airy_zeros.svg" align="middle"></span>
</p></blockquote></div>
<h5>
<a name="math_toolkit.airy.airy_root.h2"></a>
<span class="phrase"><a name="math_toolkit.airy.airy_root.examples_of_finding_airy_zeros"></a></span><a class="link" href="airy_root.html#math_toolkit.airy.airy_root.examples_of_finding_airy_zeros">Examples
@@ -312,7 +313,7 @@
<span class="identifier">OutputIterator</span> <span class="identifier">out_it</span><span class="special">);</span> <span class="comment">// Destination for zeros.</span>
</pre>
<p>
There are also versions which allows control of the <a class="link" href="../../policy.html" title="Chapter&#160;18.&#160;Policies: Controlling Precision, Error Handling etc">Policies</a>
There are also versions which allows control of the <a class="link" href="../../policy.html" title="Chapter 21. Policies: Controlling Precision, Error Handling etc">Policies</a>
for error handling and precision.
</p>
<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">OutputIterator</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Policy</span><span class="special">&gt;</span>
@@ -427,21 +428,24 @@ airy_ai_zeros:
<p>
Given the following function (A&amp;S 10.4.105):
</p>
<p>
<span class="inlinemediaobject"><img src="../../../equations/airy_zero_1.svg"></span>
</p>
<div class="blockquote"><blockquote class="blockquote"><p>
<span class="inlinemediaobject"><img src="../../../equations/airy_zero_1.svg"></span>
</p></blockquote></div>
<p>
Then an initial estimate for the n<sup>th</sup> zero a<sub>n</sub> of Ai is given by (A&amp;S 10.4.94):
</p>
<p>
<span class="inlinemediaobject"><img src="../../../equations/airy_zero_2.svg"></span>
</p>
<div class="blockquote"><blockquote class="blockquote"><p>
<span class="inlinemediaobject"><img src="../../../equations/airy_zero_2.svg"></span>
</p></blockquote></div>
<p>
and an initial estimate for the n<sup>th</sup> zero b<sub>n</sub> of Bi is given by (A&amp;S 10.4.98):
</p>
<p>
<span class="inlinemediaobject"><img src="../../../equations/airy_zero_3.svg"></span>
</p>
<div class="blockquote"><blockquote class="blockquote"><p>
<span class="inlinemediaobject"><img src="../../../equations/airy_zero_3.svg"></span>
</p></blockquote></div>
<p>
Thereafter the roots are refined using Newton iteration.
</p>
@@ -458,11 +462,11 @@ airy_ai_zeros:
</div>
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Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
Walker and Xiaogang Zhang<p>
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</p>