org.spaceroots.mantissa.algebra
Class OrthogonalPolynomial

java.lang.Object
  org.spaceroots.mantissa.algebra.Polynomial
      org.spaceroots.mantissa.algebra.Polynomial.Rational
          org.spaceroots.mantissa.algebra.OrthogonalPolynomial

All Implemented Interfaces:

Serializable

Direct Known Subclasses:

Chebyshev, Hermite, Laguerre, Legendre

public abstract class OrthogonalPolynomial

extends Polynomial.Rational

This class is the base class for orthogonal polynomials.

Orthogonal polynomials can be defined by recurrence relations like:

      O0(X)   = some 0 degree polynomial
      O1(X)   = some first degree polynomial
  a1,k Ok+1(X) = (a2,k + a3,k X) Ok(X) - a4,k Ok-1(X)
 

where a_1,k, a_2,k, a_3,k and a_4,k are simple expressions which either are constants or depend on k.

Version:

$Id: OrthogonalPolynomial.java 1711 2006-12-13 21:27:51Z luc $

Author:

L. Maisonobe

See Also:

Serialized Form

Nested Class Summary

Nested classes inherited from class org.spaceroots.mantissa.algebra.Polynomial

Polynomial.DivisionResult, Polynomial.Double, Polynomial.Rational

Field Summary

Fields inherited from class org.spaceroots.mantissa.algebra.Polynomial.Rational

a

Constructor Summary

protected

OrthogonalPolynomial(int degree, CoefficientsGenerator generator) Simple constructor.

Methods inherited from class org.spaceroots.mantissa.algebra.Polynomial.Rational

add, euclidianDivision, getCoefficients, getDegree, getDenominatorsLCM, getDerivative, isIdentity, isOne, isZero, multiply, multiply, multiply, negate, subtract, toString, valueAt

Methods inherited from class org.spaceroots.mantissa.algebra.Polynomial

divide, divide, divide, multiply

Methods inherited from class java.lang.Object

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

Constructor Detail

OrthogonalPolynomial

protected OrthogonalPolynomial(int degree,
                               CoefficientsGenerator generator)

Simple constructor. Build a degree d orthogonal polynomial

Parameters:

degree - degree of the polynomial

generator - coefficients generator for the current type of polynomials