com.numericalmethod.suanshu.analysis.uniroot

Class Halley

java.lang.Object

com.numericalmethod.suanshu.analysis.uniroot.Halley

All Implemented Interfaces:

Uniroot, java.io.Serializable

public class Halley
extends java.lang.Object
implements Uniroot

Halley's method is an iterative root finding method for a univariate function with a continuous second derivative, i.e., a C² function. It has the following properties.

• The function to be solved is assumed to be continuous and smooth (1st derivative exists).
• The 1st derivative is assumed to be continuous and smooth (2nd derivative exists).
• The rate of convergence for solution is cubic.

See Also:

Wikipedia: Halley's method, Serialized Form

Constructor Summary

Constructors

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

Method Summary

Modifier and Type	Method and Description
double	solve(UnivariateRealFunction f, double guess)
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.
double	solve(UnivariateRealFunction f, UnivariateRealFunction df, UnivariateRealFunction d2f, 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

Halley

public Halley(double tol,
              int maxIterations)

Construct an instance of Halley'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)
             throws NoRootFoundException

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

Throws:

NoRootFoundException - when the search fails to find a root

solve

public double solve(UnivariateRealFunction f,
                    double guess)
             throws NoRootFoundException

Throws:

NoRootFoundException

solve

public double solve(UnivariateRealFunction f,
                    UnivariateRealFunction df,
                    UnivariateRealFunction d2f,
                    double guess)
             throws NoRootFoundException

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

Parameters:

f - a univariate function

df - the first order derivative

d2f - the second order derivative

guess - an initial guess of the root within [lower, upper]

Returns:

an approximate root

Throws:

NoRootFoundException - when the search fails to find a root