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======拉格朗日插值======
已知$n+1$个点,可确定一个n次的线性多项式,可用拉格朗日插值求解该多项式的某一点的取值。
由公式可确定
$$f(k)=\sum_{i=1}^ny[i]\prod_{i\ne j}\frac{k-x[j]}{x[i]-x[j]}$$
由上述公式可确定该多项式的$x=k$的时候的取值$f(k)$