重节点差商的性质及其应用

Properties and applications of divided differences with repeated nodes

差商在数值逼近中是一个非常重要的工具,不同的数值逼近文献中都给予了系统介绍,并在差商的基础上定义了重节点差商,但重节点差商在不同文献中却没有系统总结.将重节点差商的几个重要性质进行了归纳,对其在构造埃米特插值中的应用进行了总结并对其理论依据进行了证明.

Divided differences are very important in numerical approximation and are introduced completely in different numerical approximations literatures.Divided differences with repeated nodes are defined on the basis of divided differences.However,they are not systematically summarized in different literatures.Some main properties of divided differences with repeated nodes are summarized,and their applications in the construction of the Hermit interpolation are also introduced and its theoretical basis has been proved.