多项式无疑是最简单，最常见的函数，

插值，不论在数学中的数值分析中，还是在我们实际生产生活中，都不难发现它的身影，比如造船业和飞机制造业中的三次样条曲线。那么，什么是插值呢？我们可以先看一下插值的定义，如下：

??（定义）如果对于每个1≤i≤n,P(xi)=yi1≤i≤n,P(xi)=yi,则称函数y=P(x)y=P(x)插值数据点(x1,y1),...,(xn,yn)(x1,y1),...,(xn,yn).

?? 插值的定义无疑是清楚明了的，而在众多的数学函数中，多项式无疑是最简单，最常见的函数，关于它的理论研究也最为透彻。因此，我们可以不妨先考虑利用多项式来进行插值。那么，这样的多项式是否总是存在呢？答案是肯定的，因为我们有如下定理：

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原文地址：https://www.cnblogs.com/hngrsgtrgrg/p/8245492.html