Polynomials::LagrangeEquidistant Class Reference

Inheritance diagram for Polynomials::LagrangeEquidistant:
Inheritance graph
[legend]

List of all members.

Public Member Functions

 LagrangeEquidistant (const unsigned int n, const unsigned int support_point)

Static Public Member Functions

static std::vector< Polynomial
< double > > 
generate_complete_basis (const unsigned int degree)

Static Private Member Functions

static std::vector< doublecompute_coefficients (const unsigned int n, const unsigned int support_point)

Detailed Description

Lagrange polynomials with equidistant interpolation points in [0,1]. The polynomial of degree n has got n+1 interpolation points. The interpolation points are sorted in ascending order. This order gives an index to each interpolation point. A Lagrangian polynomial equals to 1 at its `support point', and 0 at all other interpolation points. For example, if the degree is 3, and the support point is 1, then the polynomial represented by this object is cubic and its value is 1 at the point x=1/3, and zero at the point x=0, x=2/3, and x=1. All the polynomials have polynomial degree equal to degree, but together they span the entire space of polynomials of degree less than or equal degree.

The Lagrange polynomials are implemented up to degree 10.

Author:
Ralf Hartmann, 2000

Constructor & Destructor Documentation

Polynomials::LagrangeEquidistant::LagrangeEquidistant ( const unsigned int  n,
const unsigned int  support_point 
)

Constructor. Takes the degree n of the Lagrangian polynom and the index support_point of the support point. Fills the coefficients of the base class Polynomial.


Member Function Documentation

static std::vector<Polynomial<double> > Polynomials::LagrangeEquidistant::generate_complete_basis ( const unsigned int  degree  )  [static]

Return a vector of polynomial objects of degree degree, which then spans the full space of polynomials up to the given degree. The polynomials are generated by calling the constructor of this class with the same degree but support point running from zero to degree. This function may be used to initialize the TensorProductPolynomials and PolynomialSpace classes.

static std::vector<double> Polynomials::LagrangeEquidistant::compute_coefficients ( const unsigned int  n,
const unsigned int  support_point 
) [static, private]

Computes the coefficients of the base class Polynomial. This function is static to allow to be called in the constructor.


The documentation for this class was generated from the following file:

deal.II documentation generated on Mon Nov 23 22:58:32 2009 by doxygen 1.6.1