QuantLib: a free/open-source library for quantitative finance
fully annotated source code - version 1.34
Loading...
Searching...
No Matches
Public Member Functions | List of all members
GaussianOrthogonalPolynomial Class Referenceabstract

orthogonal polynomial for Gaussian quadratures More...

#include <gaussianorthogonalpolynomial.hpp>

+ Inheritance diagram for GaussianOrthogonalPolynomial:
+ Collaboration diagram for GaussianOrthogonalPolynomial:

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
 

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

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

Definition at line 50 of file gaussianorthogonalpolynomial.hpp.

Constructor & Destructor Documentation

◆ ~GaussianOrthogonalPolynomial()

virtual ~GaussianOrthogonalPolynomial ( )
virtualdefault

Member Function Documentation

◆ mu_0()

virtual Real mu_0 ( ) const
pure virtual

◆ alpha()

virtual Real alpha ( Size  i) const
pure virtual

◆ beta()

virtual Real beta ( Size  i) const
pure virtual

◆ w()

virtual Real w ( Real  x) const
pure virtual

◆ value()

Real value ( Size  i,
Real  x 
) const

Definition at line 32 of file gaussianorthogonalpolynomial.cpp.

+ Here is the call graph for this function:
+ Here is the caller graph for this function:

◆ weightedValue()

Real weightedValue ( Size  i,
Real  x 
) const

Definition at line 44 of file gaussianorthogonalpolynomial.cpp.

+ Here is the call graph for this function:
+ Here is the caller graph for this function: