中文摘要：

讨论了一般多点多重Hermite插值问题,给出了完全展开的多点多重Lagrange型插值公式,且就各节点重度相同的情况给出了若干特例.并利用序列对偶及广义差分方程理论等给出了计算Lagrange型插值公式的多种快速算法.

英文摘要：

This paper discusses the general Hermite interpolation problems with knots of high multiplicity and derives several Lagrange type interpolation formulas for them.As a special case,the osculating interpolation problems are also considered and the corresponding interpolation formulas are presented.Furthermore,based on dual sequence and general difference equation theories,it discusses some simple and convenient algorithms for computing Lagrange type interpolation formulas.