Documentation API of the 'org.apache.commons.math3.analysis.integration.LegendreGaussIntegrator' Java class
LegendreGaussIntegrator
org.apache.commons.math3.analysis.integration

Class LegendreGaussIntegrator

  • All Implemented Interfaces:
    UnivariateIntegrator

    Deprecated. 
    As of 3.1 (to be removed in 4.0). Please use IterativeLegendreGaussIntegrator instead.

    @Deprecatedpublic class LegendreGaussIntegratorextends BaseAbstractUnivariateIntegrator
    Implements the Legendre-Gauss quadrature formula.

    Legendre-Gauss integrators are efficient integrators that can accurately integrate functions with few function evaluations. A Legendre-Gauss integrator using an n-points quadrature formula can integrate 2n-1 degree polynomials exactly.

    These integrators evaluate the function on n carefully chosen abscissas in each step interval (mapped to the canonical [-1,1] interval). The evaluation abscissas are not evenly spaced and none of them are at the interval endpoints. This implies the function integrated can be undefined at integration interval endpoints.

    The evaluation abscissas xi are the roots of the degree n Legendre polynomial. The weights ai of the quadrature formula integrals from -1 to +1 ∫ Li2 where Li (x) = ∏ (x-xk)/(xi-xk) for k != i.

Warning: You cannot see the full API documentation of this class since the access to the DatMelt documentation for third-party Java classes is denied. Guests can only view jhplot Java API. To view the complete description of this class and its methods, please request the full DataMelt membership.

If you are already a full member, please login to the DataMelt member area before visiting this documentation.