用重节点差商法求解3n+2次Hermite插值问题

Solving the 3n+2 Orders Hermite Interpolation Problems with the Method of Difference Quotient

用重节点差商法求解Hermite插值问题,在已有的成果基础上,针对节点数完全匹配的情况,建立了带导数的Hermite插值公式,进行了相应的误差估计,并通过具体的求解例子与现有的Lagrange基函数法作了比较,显示所用方法的优越性.

This paper mainly considers the Hermite interpolation problems with the method of divided difference at the same node. Based on the existing results, it studies the Hermite interpolation functions with derivative whose number of nodes is completely matching, builds some Hermite interpolating for- mulas with derivatives, and also gives the corresponding error estimate. Some numerical examples are presented to compare the proposed method with the existing Lagrange primary function method to show its advantage.