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1、第4章插值与拟合方法插值与拟合方法是用有限个函数值去推断或表示函数的方法，它在理论数学中提到的不多。本章主要介绍有关解决这类问题的理论和方法，涉及的内容有多项式插值，分段插值及曲线拟合等。对应的方法有Lagrange插值，Newton插值，Hermite插值，分段多项式插值和线性最小二乘拟合。installationandthecablewiring,andGISandthenetworkcontrolrealestatecabinetinstallationandthecablewiring,andboilerroom,and
2、steamroominstrumenttubelaying,andboilerroom,andsteamroomBridgeframeinstallationandthecablelaying,andunitelectricdustequipmentinstallation,andcyclepumproomequipment,andpipelineinstallationandthepaint,andunitchemicalwatersystemequipmentandthepipeline1434.1实际案例4.2问题的描述与
3、基本概念先获得函数（已知或未知）在有限个点上的值……由表中数据构造一个函数P(x)作为f(x)的近似函数，去参与有关f(x)的运算。科学计算中，解决不易求出的未知函数的问题主要采用插值和拟合两种方法。installationandthecablewiring,andGISandthenetworkcontrolrealestatecabinetinstallationandthecablewiring,andboilerroom,andsteamroominstrumenttubelaying,andboilerroom,and
4、steamroomBridgeframeinstallationandthecablelaying,andunitelectricdustequipmentinstallation,andcyclepumproomequipment,andpipelineinstallationandthepaint,andunitchemicalwatersystemequipmentandthepipeline1431）插值问题的描述已知函数在[a,b]上的n+1个互异点处的函数值，求f(x)的一个近似函数P(x)，满足（4.1）称P(x)
5、为f(x)的一个插值函数，f(x)称为被插函数，点为插值节点，式（4.1）为插值条件，而误差函数称为插值余项。installationandthecablewiring,andGISandthenetworkcontrolrealestatecabinetinstallationandthecablewiring,andboilerroom,andsteamroominstrumenttubelaying,andboilerroom,andsteamroomBridgeframeinstallationandthecablela
6、ying,andunitelectricdustequipmentinstallation,andcyclepumproomequipment,andpipelineinstallationandthepaint,andunitchemicalwatersystemequipmentandthepipeline143当插值函数P(x)是多项式时称为代数插值（或多项式插值）。一个代数插值函数P(x)可写为若它满足插值条件（4.1），则有线性方程组（4.2）installationandthecablewiring,andGISan
7、dthenetworkcontrolrealestatecabinetinstallationandthecablewiring,andboilerroom,andsteamroominstrumenttubelaying,andboilerroom,andsteamroomBridgeframeinstallationandthecablelaying,andunitelectricdustequipmentinstallation,andcyclepumproomequipment,andpipelineinstallati
8、onandthepaint,andunitchemicalwatersystemequipmentandthepipeline143当m=n，它的系数行列式为范德蒙行列式因为插值节点互异，，故线性方程组（4.2）有唯一解，于是有定理4.1当插值节点互异时，存在一
