LaTeX 연습 2

$\LaTeX$ 연습용 2

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

(1) $\begin{equation*} P_{N-1}(x) = \sum_{j=0}^{N-1}{a_jx^j}\end{equation*}$

It’s cofficients $\{a_j\}$ are found as a solution of system of linear equations:

(2) $\begin{equation*} \left\{ P_{N-1} (x_k) = f_k \right\}, \quad k= -\frac{N-1}{2}, \dots , \frac{N-1}{2}\end{equation*}$

Here are references to existing equations: (1), (2).

Here is reference to non-existing equation (??).

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