math.numerics
Class Root

java.lang.Object
  math.numerics.Root

public class Root
extends java.lang.Object

Class Root defines various root finding algorithms. This class cannot be subclassed or instantiated because all methods are static.

Author:

Wolfgang Christian

Method Summary

static double	bisection(Function f, double x1, double x2, double tol) Implements the bisection method for finding the root of a function.
static double	newton(Function f, double x, double tol) Implements Newton's method for finding the root of a function.
static double	newton(Function f, Function df, double x, double tol) Implements Newton's method for finding the root of a function.
static double[]	solveQuadratic(double a, double b, double c) Solves for the roots of the quadratic equation ax2+bx+c=0.

Methods inherited from class java.lang.Object

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

Method Detail

solveQuadratic

public static double[] solveQuadratic(double a,
                                      double b,
                                      double c)

Solves for the roots of the quadratic equation ax²+bx+c=0.

Parameters:

a - double quadratic term coefficient

b - double linear term coefficient

c - double constant term

Returns:

double[] an array containing the two roots.

newton

public static double newton(Function f,
                            double x,
                            double tol)

Implements Newton's method for finding the root of a function. The derivative is calculated numerically using Romberg's method.

Parameters:

f - Function the function

x - double guess the root

tol - double computation tolerance

Returns:

double the root or NaN if root not found.

newton

public static double newton(Function f,
                            Function df,
                            double x,
                            double tol)

Implements Newton's method for finding the root of a function.

Parameters:

f - Function the function

df - Function the derivative of the function

x - double guess the root

tol - double computation tolerance

Returns:

double the root or NaN if root not found.

bisection

public static double bisection(Function f,
                               double x1,
                               double x2,
                               double tol)

Implements the bisection method for finding the root of a function.

Parameters:

f - Function the function

x - double guess root

tol - double computation tolerance

Returns:

double the root or NaN if root not found