Bisection method

<p>In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, the bisection method is a <a href="/facts/Root-finding_algorithm/IxTDkhBq">root-finding method</a> that applies to any <a href="/facts/Continuous_function/sKbl02pB">continuous function</a> for which one knows two values with opposite signs. The method consists of repeatedly <a href="/facts/Bisection/JTsya7Ca">bisecting</a> the <a href="/facts/Interval_(mathematics)/e9se3vTe">interval</a> defined by these values and then selecting the  subinterval in which the function changes sign, and therefore must contain a <a href="/facts/Root_of_a_function/mlK3dhoT">root</a>. It is a very simple and robust method, but it is also relatively slow. Because of this, it is often used to obtain a rough approximation to a solution which is then used as a starting point for more rapidly converging methods. The method is also called the interval halving method, the <a href="/facts/Binary_search_algorithm/FFmQzunc">binary search method</a>, or the dichotomy method.
</p><p>For <a href="/facts/Polynomial/Lzak8VVx">polynomials</a>, more elaborate methods exist for testing the existence of a root in an interval (<a href="/facts/Descartes%2527_rule_of_signs/DHgM49hn">Descartes' rule of signs</a>, <a href="/facts/Sturm%2527s_theorem/fn2MG3wu">Sturm's theorem</a>, <a href="/facts/Budan%2527s_theorem/TMVfNuR0">Budan's theorem</a>). They allow extending the bisection method into efficient algorithms for finding all real roots of a polynomial; see <a href="/facts/Real-root_isolation/yQ8cIVDR">Real-root isolation</a>.
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Bisection method open-in-new

Bisection method