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

Class LegendreGaussIntegrator

  • All Implemented Interfaces:

    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.

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