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<title>TheAlgorithms/C++: numerical_methods/false_position.cpp File Reference</title>
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@@ -168,8 +168,7 @@ Functions</h2></td></tr>
<div class="textblock"><p>Solve the equation \(f(x)=0\) using <a href="https://en.wikipedia.org/wiki/Regula_falsi" target="_blank">false position method</a>, also known as the Secant method. </p>
<p>First, multiple intervals are selected with the interval gap provided. Separate recursive function called for every root. Roots are printed Separatelt.</p>
<p>For an interval [a,b] \(a\) and \(b\) such that \(f(a)&lt;0\) and \(f(b)&gt;0\), then the \((i+1)^\text{th}\) approximation is given by: </p><p class="formulaDsp">
\[
x_{i+1} = \frac{a_i\cdot f(b_i) - b_i\cdot f(a_i)}{f(b_i) - f(a_i)}
\[x_{i+1} = \frac{a_i\cdot f(b_i) - b_i\cdot f(a_i)}{f(b_i) - f(a_i)}
\]
</p>
<p> For the next iteration, the interval is selected as: \([a,x]\) if \(x&gt;0\) or \([x,b]\) if \(x&lt;0\). The Process is continued till a close enough approximation is achieved.</p>
@@ -198,7 +197,7 @@ x_{i+1} = \frac{a_i\cdot f(b_i) - b_i\cdot f(a_i)}{f(b_i) - f(a_i)}
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@@ -346,7 +345,7 @@ x_{i+1} = \frac{a_i\cdot f(b_i) - b_i\cdot f(a_i)}{f(b_i) - f(a_i)}
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@@ -382,10 +381,9 @@ x_{i+1} = \frac{a_i\cdot f(b_i) - b_i\cdot f(a_i)}{f(b_i) - f(a_i)}
<div class="line"><span class="lineno"> 72</span> }</div>
<div class="line"><span class="lineno"> 73</span> <span class="keywordtype">float</span> x3 = 0, y3 = 0;</div>
<div class="line"><span class="lineno"> 74</span> x3 = x1 - (x1 - x2) * (y1) / (y1 - y2);</div>
<div class="line"><span class="lineno"> 75</span> y3 = <a class="code hl_function" href="../../d7/d6a/bisection__method_8cpp.html#a2003b5b2dcfff0769b957ab5c968b03d">eq</a>(x3);</div>
<div class="line"><span class="lineno"> 75</span> y3 = <a class="code hl_function" href="#a85a6ec58b5064d63d4f0df3854496713">eq</a>(x3);</div>
<div class="line"><span class="lineno"> 76</span> <span class="keywordflow">return</span> <a class="code hl_function" href="#a7d69b49dc37da1c02b3ab8c7fe783494">regula_falsi</a>(x2, x3, y2, y3);</div>
<div class="line"><span class="lineno"> 77</span>}</div>
<div class="ttc" id="abisection__method_8cpp_html_a2003b5b2dcfff0769b957ab5c968b03d"><div class="ttname"><a href="../../d7/d6a/bisection__method_8cpp.html#a2003b5b2dcfff0769b957ab5c968b03d">eq</a></div><div class="ttdeci">static double eq(double i)</div><div class="ttdef"><b>Definition</b> <a href="../../d7/d6a/bisection__method_8cpp_source.html#l00026">bisection_method.cpp:26</a></div></div>
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@@ -395,7 +393,7 @@ x_{i+1} = \frac{a_i\cdot f(b_i) - b_i\cdot f(a_i)}{f(b_i) - f(a_i)}
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