com.numericalmethod.suanshu.analysis.uniroot

Class Brent

java.lang.Object

com.numericalmethod.suanshu.analysis.uniroot.Brent

All Implemented Interfaces:

Uniroot, java.io.Serializable

public class Brent
extends java.lang.Object
implements Uniroot

Brent's root-finding algorithm combines super-linear convergence with reliability of bisection. It uses the secant method or inverse quadratic interpolation whenever possible because they converge faster, but falls back to the more robust bisection method if necessary. Unlike Newton and Halley, it does not need the derivatives of the function. Brent's algorithm is the preferred method of choice for root-finding.

See Also:

Wikipedia: Brent's method, Serialized Form

Constructor Summary

Constructors

Constructor and Description
Brent(double tol, int maxIterations) Construct an instance of Brent's root finding algorithm.

Method Summary

Modifier and Type	Method and Description
double	solve(UnivariateRealFunction f, double lower, double upper)
double	solve(UnivariateRealFunction f, double lower, double upper, double... guess) Search for a root, x, in the interval [lower, upper] such that f(x) = 0.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

Brent

public Brent(double tol,
             int maxIterations)

Construct an instance of Brent's root finding algorithm.

Parameters:

tol - the convergence tolerance

maxIterations - the maximum number of iterations

Method Detail

solve

public double solve(UnivariateRealFunction f,
                    double lower,
                    double upper,
                    double... guess)

Description copied from interface: Uniroot

Search for a root, x, in the interval [lower, upper] such that f(x) = 0.

Specified by:

solve in interface Uniroot

Parameters:

f - a univariate function

lower - the lower bound of the bracketing interval

upper - the upper bound of the bracketing interval

guess - an initial guess of the root within [lower, upper]. Note that guess is a double[]. This signature allows multiple initial guesses for certain types of uniroot algorithms, e.g., Brent's algorithm.

Returns:

an approximate root

solve

public double solve(UnivariateRealFunction f,
                    double lower,
                    double upper)