博客测试

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1234

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以前的博客

latex 测试

At first, we sample f(x) in the N (N is odd) equidistant points around x^<em>:
[
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*}

Its coefficients {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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f(x) + f(y) \leq f(z)

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