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.

See Also:

Serialized Form

Nested Class Summary

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

Polynomial.DivisionResult, Polynomial.Double, Polynomial.Rational

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

equals, getClass, hashCode, notify, notifyAll, wait, wait, wait