QuantLib: a free/open-source library for quantitative finance
fully annotated source code - version 1.34
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orthogonal polynomial for Gaussian quadratures More...
#include <gaussianorthogonalpolynomial.hpp>
Public Member Functions | |
virtual | ~GaussianOrthogonalPolynomial ()=default |
virtual Real | mu_0 () const =0 |
virtual Real | alpha (Size i) const =0 |
virtual Real | beta (Size i) const =0 |
virtual Real | w (Real x) const =0 |
Real | value (Size i, Real x) const |
Real | weightedValue (Size i, Real x) const |
orthogonal polynomial for Gaussian quadratures
References: Gauss quadratures and orthogonal polynomials
G.H. Gloub and J.H. Welsch: Calculation of Gauss quadrature rule. Math. Comput. 23 (1986), 221-230
"Numerical Recipes in C", 2nd edition, Press, Teukolsky, Vetterling, Flannery,
The polynomials are defined by the three-term recurrence relation
\[ P_{k+1}(x)=(x-\alpha_k) P_k(x) - \beta_k P_{k-1}(x) \]
and
\[ \mu_0 = \int{w(x)dx} \]
Definition at line 50 of file gaussianorthogonalpolynomial.hpp.
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virtualdefault |
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pure virtual |
Implemented in MomentBasedGaussianPolynomial< mp_real >, MomentBasedGaussianPolynomial< Real >, GaussLaguerrePolynomial, GaussHermitePolynomial, GaussJacobiPolynomial, GaussHyperbolicPolynomial, MomentBasedGaussianPolynomial< mp_real >, and MomentBasedGaussianPolynomial< Real >.
Implemented in GaussLaguerrePolynomial, GaussHermitePolynomial, GaussJacobiPolynomial, GaussHyperbolicPolynomial, MomentBasedGaussianPolynomial< mp_real >, MomentBasedGaussianPolynomial< Real >, MomentBasedGaussianPolynomial< mp_real >, and MomentBasedGaussianPolynomial< Real >.
Implemented in GaussLaguerrePolynomial, GaussHermitePolynomial, GaussJacobiPolynomial, GaussHyperbolicPolynomial, MomentBasedGaussianPolynomial< mp_real >, MomentBasedGaussianPolynomial< Real >, MomentBasedGaussianPolynomial< mp_real >, and MomentBasedGaussianPolynomial< Real >.
Implemented in GaussNonCentralChiSquaredPolynomial, GaussLaguerrePolynomial, GaussHermitePolynomial, GaussJacobiPolynomial, GaussHyperbolicPolynomial, GaussLaguerreCosinePolynomial< mp_real >, and GaussLaguerreSinePolynomial< mp_real >.
Definition at line 32 of file gaussianorthogonalpolynomial.cpp.
Definition at line 44 of file gaussianorthogonalpolynomial.cpp.