金巍^1，*， 谭丽^2，， 王戈^2，， 杨晓东^3，

（  1、中国酒泉卫星发射中心 兰州 732750；       2、北京科技大学 材料科学与工程学院 北京 100083；       3、国防科学与技术大学 计算机学院 长沙 410073；  ）

摘要： 拉格朗日插值多项式函数是代数多项式中一种重要的公式。其具有形式简单，对称规范的特点，便于编程运算，因此在数值计算、数据处理等方面应用得十分广泛。但是随着多项式次数的增加，它的计算复杂度也随之增加，往往带来巨大的计算量。如何快速便捷获取函数值，降低复杂度是拉格朗日插值方法研究的重要内容。本文在研究和应用拉格朗日插值算法的过程中，首次发现多项式等距节点函数值之间存在着一种规律关系，并对这一关系进行公式推导和严密的数学论证。
关键词： 计算数学；拉格朗日插值算法；多项式；等距节点

JIN Wei^1,*， TAN Li^2,， WANG Ge^2,， YANG Xiaodong^3,

（  1、Jiuquan Satellite Launch Center of China, Gansu 732750, China；       2、School of Materials Science and Engineering, University of Science and Technology Beijing, Beijing, 100083；       3、School of Computer，National University of Defense Technology，Changsha 410073，China；  ）

Abstract： The Lagrange polynomial interpolation function is one of the most important formulas of the algebric polynomials. It possesses the simple formation and gauge symmetry, which is good for programming calculation. The Lagrange interpolation method has been widely used both in fundermental and application. Such as the numerical calculation and data processing . However, with the increase of the polynomial, the complexity of algorithm is increased dramatically. So how to get the results of the function easier and faster is still an important research in this area for decreasing the complexity of algorithm. In this study, ours is the first paper to reveal the relation among the polynomial isometric nodes' function values during the application of the Lagrange interpolation algorithm. The formula is deduced which can describe the relation. Finally, the formula and it's corollary are strictly proved in the field of numerical calculation.

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