poly_differentiation()

template<typename T = double>

T integration::Integrator< T >::poly_differentiation ( int  i, int  l  )

inline

Returns the the weight needed for polynomial differentiation.

Purpose

Assuming the function \(f(x)\) is given through points \(\{(x_l,f(x_l),l=0,\dots,k)\}\)\ with \(x_{l+1}-x_{l}=h\), polynomial differentiation is defined by

\begin{align*} \frac{d}{dx}f(x)\big|_{x_i} = \frac{1}{h}\sum^k_{l=0} c_{i,l}\, f(x_l) \end{align*}

poly_differentiation returns the coefficient \(c_{i,l}\) for given indicies \(i,l\).

Parameters

i	First index of coefficients.
l	Second index of coefficients.

Definition at line 290 of file integration.hpp.

{return  poly_differentiation_[i*(k_+1)+l];}