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:

java.io.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/interfaces 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

Constructors

Modifier	Constructor and Description
protected	OrthogonalPolynomial(int degree, CoefficientsGenerator generator) Simple constructor.

Method Summary

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