SciLib.Math
Class nonLinear

java.lang.Object
  SciLib.Math.nonLinear

public final class nonLinear
extends java.lang.Object

This class contains some nolinear methods

Constructor Summary

nonLinear()

Method Summary

static double	bisect(Function f, double a, double b, double epsi) Bisection method for solving nonlinear equation
static double	bisect(Function f, double a, double b, int n) Bisection method for solving nonlinear equation
static double[]	coef(double[] px, double[] py) Compute the coefficients by divided difference
static double	eval(double[] a, double[] px, int n, double x) Compute the value of polynom with Horner's rule
static double	lagrangeInterpolation(double[] px, double[] py, double x) Interpoaltion by Lagrange method
static double	newton(Function f, Function deriv, double x, double epsi) Newton method for solving nonlinear equation
static double	newton(Function f, Function deriv, double x, int n) Newton method for solving nonlinear equation
static double	richardsonExtrapolation(Function f, double x, double h, int n) Compute Derivative of a function f at x by the Richardson Extrapolation method
static double	richardsonExtrapolation(Function f, double x, int n) Compute the derivative of a function f at x by the Richardson Extrapolation method
static double	richardsonExtrapolation2deriv(Function f, double x, double h, int n) Compute the second derivative of a function f at x by the Richardson Extrapolation method
static double	Romberg(Function f, float a, float b, int n) Compute the integration by Romberg method
static double	secant(Function f, double a, double b, double epsi) Secant method for solving nonlinear equation
static double	secant(Function f, double a, double b, int n) Secant method for solving nonlinear equation
static double	trape(Function f, float a, float b, int n) Compute the integration by Trape method

Methods inherited from class java.lang.Object

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

Constructor Detail

nonLinear

public nonLinear()

Method Detail

bisect

public static double bisect(Function f,
                            double a,
                            double b,
                            int n)

Bisection method for solving nonlinear equation

Parameters:

f - nonlinear function

a - A double value, the left point

b - A double value, the right point

n - An integer value, the numbers of iteration

Returns:

a double value, the zero of the equation between a and b

bisect

public static double bisect(Function f,
                            double a,
                            double b,
                            double epsi)

Bisection method for solving nonlinear equation

Parameters:

f - nonlinear function

a - A double value, the left point

b - A double value, the right point

epsi - A double value, the error

Returns:

a double value, the zero of the equation between a and b

newton

public static double newton(Function f,
                            Function deriv,
                            double x,
                            int n)

Newton method for solving nonlinear equation

Parameters:

f - nonlinear function

deriv - a function, the derivative of f

x - A double value, the start point

n - An integer value, the numbers of iteration

Returns:

a double value, A zero of the equation

newton

public static double newton(Function f,
                            Function deriv,
                            double x,
                            double epsi)

Newton method for solving nonlinear equation

Parameters:

f - nonlinear function

deriv - a function, the derivative of f

x - A double value, the start point

epsi - A double value, the error

Returns:

a double value, A zero of the equation

secant

public static double secant(Function f,
                            double a,
                            double b,
                            int n)

Secant method for solving nonlinear equation

Parameters:

f - nonlinear function

a - A double value, the left point

b - A double value, the right point

n - An integer value, the numbers of iteration

Returns:

a double value, the zero of the equation between a and b

secant

public static double secant(Function f,
                            double a,
                            double b,
                            double epsi)

Secant method for solving nonlinear equation

Parameters:

f - nonlinear function

a - A double value, the left point

b - A double value, the right point

epsi - A double value, the error

Returns:

a double value, the zero of the equation between a and b

richardsonExtrapolation

public static double richardsonExtrapolation(Function f,
                                             double x,
                                             double h,
                                             int n)

Compute Derivative of a function f at x by the Richardson Extrapolation method

Parameters:

f - nonlinear function

x - A double value

h - A double value

n - An integer value, the numbers of iteration

Returns:

a double value, the zero of the equation between a and b

richardsonExtrapolation

public static double richardsonExtrapolation(Function f,
                                             double x,
                                             int n)

Compute the derivative of a function f at x by the Richardson Extrapolation method

Parameters:

f - nonlinear function

x - A double value

n - An integer value, the numbers of iteration

Returns:

a double value, the zero of the equation between a and b

richardsonExtrapolation2deriv

public static double richardsonExtrapolation2deriv(Function f,
                                                   double x,
                                                   double h,
                                                   int n)

Compute the second derivative of a function f at x by the Richardson Extrapolation method

Parameters:

f - nonlinear function

x - A double value

h - A double value

n - An integer value, the numbers of iteration

Returns:

a double value, the zero of the equation between a and b

coef

public static double[] coef(double[] px,
                            double[] py)

Compute the coefficients by divided difference

eval

public static double eval(double[] a,
                          double[] px,
                          int n,
                          double x)

Compute the value of polynom with Horner's rule

lagrangeInterpolation

public static double lagrangeInterpolation(double[] px,
                                           double[] py,
                                           double x)

Interpoaltion by Lagrange method

trape

public static double trape(Function f,
                           float a,
                           float b,
                           int n)

Compute the integration by Trape method

Romberg

public static double Romberg(Function f,
                             float a,
                             float b,
                             int n)

Compute the integration by Romberg method