GaussianOrthogonalPolynomial Class Reference

#include <ql/math/integrals/gaussianorthogonalpolynomial.hpp>

Inheritance diagram for GaussianOrthogonalPolynomial:

Inheritance graph
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List of all members.

Detailed Description

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

\[ \mu_0 = \int{w(x)dx} \]


Public Member Functions

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