Package org.apache.commons.math.analysis.polynomials

Class PolynomialsUtils

java.lang.Object

org.apache.commons.math.analysis.polynomials.PolynomialsUtils

public class PolynomialsUtils
extends java.lang.Object

A collection of static methods that operate on or return polynomials.

Since:

2.0

Version:

$Revision: 990655 $ $Date: 2010-08-29 23:49:40 +0200 (dim. 29 août 2010) $

Method Summary

Modifier and Type	Method	Description
static PolynomialFunction	createChebyshevPolynomial(int degree)	Create a Chebyshev polynomial of the first kind.
static PolynomialFunction	createHermitePolynomial(int degree)	Create a Hermite polynomial.
static PolynomialFunction	createLaguerrePolynomial(int degree)	Create a Laguerre polynomial.
static PolynomialFunction	createLegendrePolynomial(int degree)	Create a Legendre polynomial.

Methods inherited from class java.lang.Object

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

Method Detail

createChebyshevPolynomial

public static PolynomialFunction createChebyshevPolynomial(int degree)

Create a Chebyshev polynomial of the first kind.

Chebyshev polynomials of the first kind are orthogonal polynomials. They can be defined by the following recurrence relations:

  T0(X)   = 1
  T1(X)   = X
  Tk+1(X) = 2X Tk(X) - Tk-1(X)
 

Parameters:

degree - degree of the polynomial

Returns:

Chebyshev polynomial of specified degree

createHermitePolynomial

public static PolynomialFunction createHermitePolynomial(int degree)

Create a Hermite polynomial.

Hermite polynomials are orthogonal polynomials. They can be defined by the following recurrence relations:

  H0(X)   = 1
  H1(X)   = 2X
  Hk+1(X) = 2X Hk(X) - 2k Hk-1(X)
 

Parameters:

degree - degree of the polynomial

Returns:

Hermite polynomial of specified degree

createLaguerrePolynomial

public static PolynomialFunction createLaguerrePolynomial(int degree)

Create a Laguerre polynomial.

Laguerre polynomials are orthogonal polynomials. They can be defined by the following recurrence relations:

        L0(X)   = 1
        L1(X)   = 1 - X
  (k+1) Lk+1(X) = (2k + 1 - X) Lk(X) - k Lk-1(X)
 

Parameters:

degree - degree of the polynomial

Returns:

Laguerre polynomial of specified degree

createLegendrePolynomial

public static PolynomialFunction createLegendrePolynomial(int degree)

Create a Legendre polynomial.

Legendre polynomials are orthogonal polynomials. They can be defined by the following recurrence relations:

        P0(X)   = 1
        P1(X)   = X
  (k+1) Pk+1(X) = (2k+1) X Pk(X) - k Pk-1(X)
 

Parameters:

degree - degree of the polynomial

Returns:

Legendre polynomial of specified degree