Class 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 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