Class PolynomialsUtils

java.lang.Object
org.apache.commons.math.analysis.polynomials.PolynomialsUtils

public class PolynomialsUtils extends 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 Details

    • 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