[latexpage]At first, we sample $f(x)$ in the $N$ ($N$ is odd) equidistant points around $x^*$:\[ f_k = f(x_k),\: x_k = x^*+kh,\: k=-\frac{N-1}{2},\dots,\frac{N-1}{2}\]where $h$ is some step.Then we interpolate points $\{(x_k,f_k)\}$ by polynomial\begin{equation} \label{eq:poly} P_{N-1}(x)=\sum_{j=0}^{N-1}{a_jx^j}\end{equation}Its coefficients $\{a_j\}$ are found as a solution of system of linear equations:\begin{equation} \label{eq:sys} \left\{ P_{N-1}(x_k) = f_k\right\},\quad k=-\frac{N-1}{2},\dots,\frac{N-1}{2}\end{equation}Here are references to existing equations: (\ref{eq:poly}), (\ref{eq:sys}).Here is […]
