poly_interpolation()

template<typename T = double>

T integration::Integrator< T >::poly_interpolation ( int  alpha, int  l  )

inline

Returns the the weight needed for polynomial interpolation.

Purpose

The \(k\)-th order approximation polynomial \(P(x)\) through function values \(\{(x_l,f(x_l),l=0,\dots,k)\}\) with \(x_{l+1}-x_{l}=h\) is given by

\begin{align*} P(x) = \sum^k_{\alpha=0}\sum^k_{l=0} c_{\alpha,l}\, \left(\frac{x}{h}\right)^\alpha f(x_l) \end{align*}

poly_interpolation returns the coeffient \(c_{\alpha,l}\) for given indicies \(\alpha,l\).

Parameters

alpha	First index of coefficients.
l	Second index of coefficients.

Definition at line 262 of file integration.hpp.

{return  poly_interpolation_[alpha*(k_+1)+l];}