<title>Root Finding Without Derivatives</title>
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+<link rel="home" href="../index.html" title="Math Toolkit 2.11.0">
+<link rel="up" href="../root_finding.html" title="Chapter 10. Root Finding & Minimization Algorithms">
+<link rel="prev" href="../root_finding.html" title="Chapter 10. Root Finding & Minimization Algorithms">
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<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">tools</span><span class="special">/</span><span class="identifier">roots</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span>
</pre>
-<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span> <span class="special">{</span>
-<span class="keyword">namespace</span> <span class="identifier">tools</span> <span class="special">{</span> <span class="comment">// Note namespace boost::math::tools.</span>
-<span class="comment">// Bisection</span>
-<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">F</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Tol</span><span class="special">></span>
-<span class="identifier">std</span><span class="special">::</span><span class="identifier">pair</span><span class="special"><</span><span class="identifier">T</span><span class="special">,</span> <span class="identifier">T</span><span class="special">></span>
- <span class="identifier">bisect</span><span class="special">(</span>
- <span class="identifier">F</span> <span class="identifier">f</span><span class="special">,</span>
- <span class="identifier">T</span> <span class="identifier">min</span><span class="special">,</span>
- <span class="identifier">T</span> <span class="identifier">max</span><span class="special">,</span>
- <span class="identifier">Tol</span> <span class="identifier">tol</span><span class="special">,</span>
- <span class="identifier">boost</span><span class="special">::</span><span class="identifier">uintmax_t</span><span class="special">&</span> <span class="identifier">max_iter</span><span class="special">);</span>
+<pre class="programlisting"> <span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span> <span class="special">{</span>
+ <span class="keyword">namespace</span> <span class="identifier">tools</span> <span class="special">{</span> <span class="comment">// Note namespace boost::math::tools.</span>
+ <span class="comment">// Bisection</span>
+ <span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">F</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Tol</span><span class="special">></span>
+ <span class="identifier">std</span><span class="special">::</span><span class="identifier">pair</span><span class="special"><</span><span class="identifier">T</span><span class="special">,</span> <span class="identifier">T</span><span class="special">></span>
+ <span class="identifier">bisect</span><span class="special">(</span>
+ <span class="identifier">F</span> <span class="identifier">f</span><span class="special">,</span>
+ <span class="identifier">T</span> <span class="identifier">min</span><span class="special">,</span>
+ <span class="identifier">T</span> <span class="identifier">max</span><span class="special">,</span>
+ <span class="identifier">Tol</span> <span class="identifier">tol</span><span class="special">,</span>
+ <span class="identifier">boost</span><span class="special">::</span><span class="identifier">uintmax_t</span><span class="special">&</span> <span class="identifier">max_iter</span><span class="special">);</span>
-<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">F</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Tol</span><span class="special">></span>
-<span class="identifier">std</span><span class="special">::</span><span class="identifier">pair</span><span class="special"><</span><span class="identifier">T</span><span class="special">,</span> <span class="identifier">T</span><span class="special">></span>
- <span class="identifier">bisect</span><span class="special">(</span>
- <span class="identifier">F</span> <span class="identifier">f</span><span class="special">,</span>
- <span class="identifier">T</span> <span class="identifier">min</span><span class="special">,</span>
- <span class="identifier">T</span> <span class="identifier">max</span><span class="special">,</span>
- <span class="identifier">Tol</span> <span class="identifier">tol</span><span class="special">);</span>
+ <span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">F</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Tol</span><span class="special">></span>
+ <span class="identifier">std</span><span class="special">::</span><span class="identifier">pair</span><span class="special"><</span><span class="identifier">T</span><span class="special">,</span> <span class="identifier">T</span><span class="special">></span>
+ <span class="identifier">bisect</span><span class="special">(</span>
+ <span class="identifier">F</span> <span class="identifier">f</span><span class="special">,</span>
+ <span class="identifier">T</span> <span class="identifier">min</span><span class="special">,</span>
+ <span class="identifier">T</span> <span class="identifier">max</span><span class="special">,</span>
+ <span class="identifier">Tol</span> <span class="identifier">tol</span><span class="special">);</span>
-<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">F</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Tol</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../policy.html" title="Chapter 19. Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">></span>
-<span class="identifier">std</span><span class="special">::</span><span class="identifier">pair</span><span class="special"><</span><span class="identifier">T</span><span class="special">,</span> <span class="identifier">T</span><span class="special">></span>
- <span class="identifier">bisect</span><span class="special">(</span>
- <span class="identifier">F</span> <span class="identifier">f</span><span class="special">,</span>
- <span class="identifier">T</span> <span class="identifier">min</span><span class="special">,</span>
- <span class="identifier">T</span> <span class="identifier">max</span><span class="special">,</span>
- <span class="identifier">Tol</span> <span class="identifier">tol</span><span class="special">,</span>
- <span class="identifier">boost</span><span class="special">::</span><span class="identifier">uintmax_t</span><span class="special">&</span> <span class="identifier">max_iter</span><span class="special">,</span>
- <span class="keyword">const</span> <a class="link" href="../policy.html" title="Chapter 19. Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&);</span>
+ <span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">F</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Tol</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../policy.html" title="Chapter 20. Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">></span>
+ <span class="identifier">std</span><span class="special">::</span><span class="identifier">pair</span><span class="special"><</span><span class="identifier">T</span><span class="special">,</span> <span class="identifier">T</span><span class="special">></span>
+ <span class="identifier">bisect</span><span class="special">(</span>
+ <span class="identifier">F</span> <span class="identifier">f</span><span class="special">,</span>
+ <span class="identifier">T</span> <span class="identifier">min</span><span class="special">,</span>
+ <span class="identifier">T</span> <span class="identifier">max</span><span class="special">,</span>
+ <span class="identifier">Tol</span> <span class="identifier">tol</span><span class="special">,</span>
+ <span class="identifier">boost</span><span class="special">::</span><span class="identifier">uintmax_t</span><span class="special">&</span> <span class="identifier">max_iter</span><span class="special">,</span>
+ <span class="keyword">const</span> <a class="link" href="../policy.html" title="Chapter 20. Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&);</span>
-<span class="comment">// Bracket and Solve Root</span>
-<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">F</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Tol</span><span class="special">></span>
-<span class="identifier">std</span><span class="special">::</span><span class="identifier">pair</span><span class="special"><</span><span class="identifier">T</span><span class="special">,</span> <span class="identifier">T</span><span class="special">></span>
- <span class="identifier">bracket_and_solve_root</span><span class="special">(</span>
- <span class="identifier">F</span> <span class="identifier">f</span><span class="special">,</span>
- <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&</span> <span class="identifier">guess</span><span class="special">,</span>
- <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&</span> <span class="identifier">factor</span><span class="special">,</span>
- <span class="keyword">bool</span> <span class="identifier">rising</span><span class="special">,</span>
- <span class="identifier">Tol</span> <span class="identifier">tol</span><span class="special">,</span>
- <span class="identifier">boost</span><span class="special">::</span><span class="identifier">uintmax_t</span><span class="special">&</span> <span class="identifier">max_iter</span><span class="special">);</span>
+ <span class="comment">// Bracket and Solve Root</span>
+ <span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">F</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Tol</span><span class="special">></span>
+ <span class="identifier">std</span><span class="special">::</span><span class="identifier">pair</span><span class="special"><</span><span class="identifier">T</span><span class="special">,</span> <span class="identifier">T</span><span class="special">></span>
+ <span class="identifier">bracket_and_solve_root</span><span class="special">(</span>
+ <span class="identifier">F</span> <span class="identifier">f</span><span class="special">,</span>
+ <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&</span> <span class="identifier">guess</span><span class="special">,</span>
+ <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&</span> <span class="identifier">factor</span><span class="special">,</span>
+ <span class="keyword">bool</span> <span class="identifier">rising</span><span class="special">,</span>
+ <span class="identifier">Tol</span> <span class="identifier">tol</span><span class="special">,</span>
+ <span class="identifier">boost</span><span class="special">::</span><span class="identifier">uintmax_t</span><span class="special">&</span> <span class="identifier">max_iter</span><span class="special">);</span>
-<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">F</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Tol</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../policy.html" title="Chapter 19. Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">></span>
-<span class="identifier">std</span><span class="special">::</span><span class="identifier">pair</span><span class="special"><</span><span class="identifier">T</span><span class="special">,</span> <span class="identifier">T</span><span class="special">></span>
- <span class="identifier">bracket_and_solve_root</span><span class="special">(</span>
- <span class="identifier">F</span> <span class="identifier">f</span><span class="special">,</span>
- <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&</span> <span class="identifier">guess</span><span class="special">,</span>
- <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&</span> <span class="identifier">factor</span><span class="special">,</span>
- <span class="keyword">bool</span> <span class="identifier">rising</span><span class="special">,</span>
- <span class="identifier">Tol</span> <span class="identifier">tol</span><span class="special">,</span>
- <span class="identifier">boost</span><span class="special">::</span><span class="identifier">uintmax_t</span><span class="special">&</span> <span class="identifier">max_iter</span><span class="special">,</span>
- <span class="keyword">const</span> <a class="link" href="../policy.html" title="Chapter 19. Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&);</span>
+ <span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">F</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Tol</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../policy.html" title="Chapter 20. Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">></span>
+ <span class="identifier">std</span><span class="special">::</span><span class="identifier">pair</span><span class="special"><</span><span class="identifier">T</span><span class="special">,</span> <span class="identifier">T</span><span class="special">></span>
+ <span class="identifier">bracket_and_solve_root</span><span class="special">(</span>
+ <span class="identifier">F</span> <span class="identifier">f</span><span class="special">,</span>
+ <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&</span> <span class="identifier">guess</span><span class="special">,</span>
+ <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&</span> <span class="identifier">factor</span><span class="special">,</span>
+ <span class="keyword">bool</span> <span class="identifier">rising</span><span class="special">,</span>
+ <span class="identifier">Tol</span> <span class="identifier">tol</span><span class="special">,</span>
+ <span class="identifier">boost</span><span class="special">::</span><span class="identifier">uintmax_t</span><span class="special">&</span> <span class="identifier">max_iter</span><span class="special">,</span>
+ <span class="keyword">const</span> <a class="link" href="../policy.html" title="Chapter 20. Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&);</span>
- <span class="comment">// TOMS 748 algorithm</span>
-<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">F</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Tol</span><span class="special">></span>
-<span class="identifier">std</span><span class="special">::</span><span class="identifier">pair</span><span class="special"><</span><span class="identifier">T</span><span class="special">,</span> <span class="identifier">T</span><span class="special">></span>
- <span class="identifier">toms748_solve</span><span class="special">(</span>
- <span class="identifier">F</span> <span class="identifier">f</span><span class="special">,</span>
- <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&</span> <span class="identifier">a</span><span class="special">,</span>
- <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&</span> <span class="identifier">b</span><span class="special">,</span>
- <span class="identifier">Tol</span> <span class="identifier">tol</span><span class="special">,</span>
- <span class="identifier">boost</span><span class="special">::</span><span class="identifier">uintmax_t</span><span class="special">&</span> <span class="identifier">max_iter</span><span class="special">);</span>
+<span class="comment">// TOMS 748 algorithm</span>
+ <span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">F</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Tol</span><span class="special">></span>
+ <span class="identifier">std</span><span class="special">::</span><span class="identifier">pair</span><span class="special"><</span><span class="identifier">T</span><span class="special">,</span> <span class="identifier">T</span><span class="special">></span>
+ <span class="identifier">toms748_solve</span><span class="special">(</span>
+ <span class="identifier">F</span> <span class="identifier">f</span><span class="special">,</span>
+ <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&</span> <span class="identifier">a</span><span class="special">,</span>
+ <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&</span> <span class="identifier">b</span><span class="special">,</span>
+ <span class="identifier">Tol</span> <span class="identifier">tol</span><span class="special">,</span>
+ <span class="identifier">boost</span><span class="special">::</span><span class="identifier">uintmax_t</span><span class="special">&</span> <span class="identifier">max_iter</span><span class="special">);</span>
-<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">F</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Tol</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../policy.html" title="Chapter 19. Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">></span>
-<span class="identifier">std</span><span class="special">::</span><span class="identifier">pair</span><span class="special"><</span><span class="identifier">T</span><span class="special">,</span> <span class="identifier">T</span><span class="special">></span>
- <span class="identifier">toms748_solve</span><span class="special">(</span>
- <span class="identifier">F</span> <span class="identifier">f</span><span class="special">,</span>
- <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&</span> <span class="identifier">a</span><span class="special">,</span>
- <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&</span> <span class="identifier">b</span><span class="special">,</span>
- <span class="identifier">Tol</span> <span class="identifier">tol</span><span class="special">,</span>
- <span class="identifier">boost</span><span class="special">::</span><span class="identifier">uintmax_t</span><span class="special">&</span> <span class="identifier">max_iter</span><span class="special">,</span>
- <span class="keyword">const</span> <a class="link" href="../policy.html" title="Chapter 19. Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&);</span>
+ <span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">F</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Tol</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../policy.html" title="Chapter 20. Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">></span>
+ <span class="identifier">std</span><span class="special">::</span><span class="identifier">pair</span><span class="special"><</span><span class="identifier">T</span><span class="special">,</span> <span class="identifier">T</span><span class="special">></span>
+ <span class="identifier">toms748_solve</span><span class="special">(</span>
+ <span class="identifier">F</span> <span class="identifier">f</span><span class="special">,</span>
+ <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&</span> <span class="identifier">a</span><span class="special">,</span>
+ <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&</span> <span class="identifier">b</span><span class="special">,</span>
+ <span class="identifier">Tol</span> <span class="identifier">tol</span><span class="special">,</span>
+ <span class="identifier">boost</span><span class="special">::</span><span class="identifier">uintmax_t</span><span class="special">&</span> <span class="identifier">max_iter</span><span class="special">,</span>
+ <span class="keyword">const</span> <a class="link" href="../policy.html" title="Chapter 20. Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&);</span>
-<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">F</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Tol</span><span class="special">></span>
-<span class="identifier">std</span><span class="special">::</span><span class="identifier">pair</span><span class="special"><</span><span class="identifier">T</span><span class="special">,</span> <span class="identifier">T</span><span class="special">></span>
- <span class="identifier">toms748_solve</span><span class="special">(</span>
- <span class="identifier">F</span> <span class="identifier">f</span><span class="special">,</span>
- <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&</span> <span class="identifier">a</span><span class="special">,</span>
- <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&</span> <span class="identifier">b</span><span class="special">,</span>
- <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&</span> <span class="identifier">fa</span><span class="special">,</span>
- <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&</span> <span class="identifier">fb</span><span class="special">,</span>
- <span class="identifier">Tol</span> <span class="identifier">tol</span><span class="special">,</span>
- <span class="identifier">boost</span><span class="special">::</span><span class="identifier">uintmax_t</span><span class="special">&</span> <span class="identifier">max_iter</span><span class="special">);</span>
+ <span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">F</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Tol</span><span class="special">></span>
+ <span class="identifier">std</span><span class="special">::</span><span class="identifier">pair</span><span class="special"><</span><span class="identifier">T</span><span class="special">,</span> <span class="identifier">T</span><span class="special">></span>
+ <span class="identifier">toms748_solve</span><span class="special">(</span>
+ <span class="identifier">F</span> <span class="identifier">f</span><span class="special">,</span>
+ <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&</span> <span class="identifier">a</span><span class="special">,</span>
+ <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&</span> <span class="identifier">b</span><span class="special">,</span>
+ <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&</span> <span class="identifier">fa</span><span class="special">,</span>
+ <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&</span> <span class="identifier">fb</span><span class="special">,</span>
+ <span class="identifier">Tol</span> <span class="identifier">tol</span><span class="special">,</span>
+ <span class="identifier">boost</span><span class="special">::</span><span class="identifier">uintmax_t</span><span class="special">&</span> <span class="identifier">max_iter</span><span class="special">);</span>
-<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">F</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Tol</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../policy.html" title="Chapter 19. Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">></span>
-<span class="identifier">std</span><span class="special">::</span><span class="identifier">pair</span><span class="special"><</span><span class="identifier">T</span><span class="special">,</span> <span class="identifier">T</span><span class="special">></span>
- <span class="identifier">toms748_solve</span><span class="special">(</span>
- <span class="identifier">F</span> <span class="identifier">f</span><span class="special">,</span>
- <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&</span> <span class="identifier">a</span><span class="special">,</span>
- <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&</span> <span class="identifier">b</span><span class="special">,</span>
- <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&</span> <span class="identifier">fa</span><span class="special">,</span>
- <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&</span> <span class="identifier">fb</span><span class="special">,</span>
- <span class="identifier">Tol</span> <span class="identifier">tol</span><span class="special">,</span>
- <span class="identifier">boost</span><span class="special">::</span><span class="identifier">uintmax_t</span><span class="special">&</span> <span class="identifier">max_iter</span><span class="special">,</span>
- <span class="keyword">const</span> <a class="link" href="../policy.html" title="Chapter 19. Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&);</span>
+ <span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">F</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Tol</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../policy.html" title="Chapter 20. Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">></span>
+ <span class="identifier">std</span><span class="special">::</span><span class="identifier">pair</span><span class="special"><</span><span class="identifier">T</span><span class="special">,</span> <span class="identifier">T</span><span class="special">></span>
+ <span class="identifier">toms748_solve</span><span class="special">(</span>
+ <span class="identifier">F</span> <span class="identifier">f</span><span class="special">,</span>
+ <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&</span> <span class="identifier">a</span><span class="special">,</span>
+ <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&</span> <span class="identifier">b</span><span class="special">,</span>
+ <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&</span> <span class="identifier">fa</span><span class="special">,</span>
+ <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&</span> <span class="identifier">fb</span><span class="special">,</span>
+ <span class="identifier">Tol</span> <span class="identifier">tol</span><span class="special">,</span>
+ <span class="identifier">boost</span><span class="special">::</span><span class="identifier">uintmax_t</span><span class="special">&</span> <span class="identifier">max_iter</span><span class="special">,</span>
+ <span class="keyword">const</span> <a class="link" href="../policy.html" title="Chapter 20. Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&);</span>
-<span class="comment">// Termination conditions:</span>
-<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">></span>
-<span class="keyword">struct</span> <span class="identifier">eps_tolerance</span><span class="special">;</span>
+ <span class="comment">// Termination conditions:</span>
+ <span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">></span>
+ <span class="keyword">struct</span> <span class="identifier">eps_tolerance</span><span class="special">;</span>
-<span class="keyword">struct</span> <span class="identifier">equal_floor</span><span class="special">;</span>
-<span class="keyword">struct</span> <span class="identifier">equal_ceil</span><span class="special">;</span>
-<span class="keyword">struct</span> <span class="identifier">equal_nearest_integer</span><span class="special">;</span>
+ <span class="keyword">struct</span> <span class="identifier">equal_floor</span><span class="special">;</span>
+ <span class="keyword">struct</span> <span class="identifier">equal_ceil</span><span class="special">;</span>
+ <span class="keyword">struct</span> <span class="identifier">equal_nearest_integer</span><span class="special">;</span>
-<span class="special">}}}</span> <span class="comment">// boost::math::tools namespaces</span>
+ <span class="special">}}}</span> <span class="comment">// boost::math::tools namespaces</span>
</pre>
<h5>
<a name="math_toolkit.roots_noderiv.h1"></a>
functions use <a class="link" href="roots_noderiv/TOMS748.html" title="Algorithm TOMS 748: Alefeld, Potra and Shi: Enclosing zeros of continuous functions">TOMS 748 algorithm</a>
by Alefeld, Potra and Shi that is asymptotically the most efficient known,
and has been shown to be optimal for a certain classes of smooth functions.
- Variants with and without <a class="link" href="../policy.html" title="Chapter 19. Policies: Controlling Precision, Error Handling etc">Policies</a> are provided.
+ Variants with and without <a class="link" href="../policy.html" title="Chapter 20. Policies: Controlling Precision, Error Handling etc">Policies</a> are provided.
</p>
<p>
Alternatively, <a class="link" href="roots_noderiv/bisect.html" title="Bisection">bisect</a>
projects / platform / upstream / boost.git / blobdiff