org.jscience.mathematics.analysis.polynomials
Interface OrthogonalPolynomialFactory

All Known Implementing Classes:

ChebyshevDoublePolynomialFactory, GegenbauerDoublePolynomialFactory, HermiteDoublePolynomialFactory, JacobiDoublePolynomialFactory, LaguerreDoublePolynomialFactory, LegendreDoublePolynomialFactory, OrthogonalDoublePolynomialFactory, OrthogonalExactRealPolynomialFactory, SecondKindChebyshevDoublePolynomialFactory

public interface OrthogonalPolynomialFactory

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
  a1k Ok+1(X) = (a2k + a3k X) Ok(X) - a4k Ok-1(X)
 

where a0k, a1k, a2k and a3k are simple expressions which either are constants or depend on k.

Method Summary

Polynomial[]	getFirstTermsPolynomials() Initialize the recurrence coefficients for degree 0 and 1.
Polynomial	getOrthogonalPolynomial(int degree) DOCUMENT ME!
Field.Member[]	getRecurrenceCoefficients(int k) Initialize the recurrence coefficients.

Method Detail

getOrthogonalPolynomial

Polynomial getOrthogonalPolynomial(int degree)

DOCUMENT ME!

Parameters:

degree - DOCUMENT ME!

Returns:

DOCUMENT ME!

getFirstTermsPolynomials

Polynomial[] getFirstTermsPolynomials()

Initialize the recurrence coefficients for degree 0 and 1.

Returns:

an array which contains the coefficients for degree 0 and 1

getRecurrenceCoefficients

Field.Member[] getRecurrenceCoefficients(int k)

Initialize the recurrence coefficients. The recurrence relation is

a1k Ok+1(X) = (a2k + a3k X) Ok(X) - a4k Ok-1(X)

Parameters:

k - index of the current step

Returns:

a double array of 3 elements: b2k = double[0] coefficient to initialize (b2k = a2k / a1k) b3k = double[1] coefficient to initialize (b3k = a3k / a1k) b4k = double[2] coefficient to initialize (b4k = a4k / a1k)