Integration test post

Thoth Association for Mathematics and Sciences

Integration test post

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_kright},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 reference to non-existing equation (ref{eq:unknown}).

 

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