brent.hpp File Reference

#include <suanPan.h>

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Functions
template<std::floating_point T, std::invocable< T > F>
T	brent (F &&func, const T x1, const T x2, const T tol)
	Implements Brent's method for finding a root of a function within a given interval.

Function Documentation

brent()

template<std::floating_point T, std::invocable< T > F>

T brent	(	F &&	func,
		const T	x1,
		const T	x2,
		const T	tol
	)

Implements Brent's method for finding a root of a function within a given interval.

Brent's method combines the bisection method, the secant method, and inverse quadratic interpolation to efficiently find a root of a function. It is robust and guarantees convergence as long as the function changes sign over the interval [x1, x2].

Template Parameters

T	The floating-point type (e.g., float, double, long double).
F	The callable type representing the function to find the root of. Must accept a single argument of type T and return a value of type T.

Parameters

func	The function for which the root is to be found. It must be continuous and change sign over the interval [x1, x2].
x1	The lower bound of the interval.
x2	The upper bound of the interval.
tol	The desired tolerance for the root. The algorithm stops when the root is found to this precision.

Returns

The approximate root of the function within the given interval and tolerance.

Note

The function assumes that the initial interval [x1, x2] contains a root (i.e., func(x1) and func(x2) have opposite signs). If this condition is not met, the behavior is undefined.

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