Brent's method

<p>In <a href="/facts/Numerical_analysis/QT9cYa9z">numerical analysis</a>, Brent's method is a hybrid <a href="/facts/Root-finding_algorithm/IxTDkhBq">root-finding algorithm</a> combining the <a href="/facts/Bisection_method/3tWmtoIp">bisection method</a>, the <a href="/facts/Secant_method/tkNV8Rzk">secant method</a> and <a href="/facts/Inverse_quadratic_interpolation/7fQrKtYn">inverse quadratic interpolation</a>. It has the reliability of bisection but it can be as quick as some of the less-reliable methods. The algorithm tries to use the potentially fast-converging secant method or inverse quadratic interpolation if possible, but it falls back to the more robust bisection method if necessary. Brent's method is due to <a href="/facts/Richard_Brent_(scientist)/JYLmuA0M">Richard Brent</a> and builds on an earlier algorithm by <a href="/facts/Theodorus_Dekker/L0ALFPKz">Theodorus Dekker</a>. Consequently, the method is also known as the Brent–Dekker method.
</p><p>Modern improvements on Brent's method include Chandrupatla's method, which is simpler and faster for functions that are flat around their roots; <a href="/facts/Ridders%2527_method/4wgrjMwn">Ridders' method</a>, which performs exponential interpolations instead of quadratic providing a simpler closed formula for the iterations; and the <a href="/facts/ITP_Method/tPzXpXEA">ITP method</a> which is a hybrid between regula-falsi and bisection that achieves optimal worst-case and asymptotic guarantees.
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Brent's method open-in-new

Brent's method