一类多元Hermite型插值的离散化问题

利用离散逼近算法理论, 研究一类特殊的多元Hermite型插值的离散化问题, 即将给定的Hermite型插值问题离散为一列Lagrange插值问题的极限. 当Hermite型插值问题的插值条件对应一个二阶微分不变子空间时, 利用其空间的结构属性, 给出该问题在离散逼近算法思想下可被离散的充要条件, 该条件对应的非线性方程组规模较小, 计算效率较高.

Discretization Problems of a Class of Multivariate Hermite-Type Interpolation

We studied the discretization problems of a special class of  multivariate Hermite-type interpolation by using  the theory of discrete approximation algorithm. Namely,  a given Hermite-type interpolation problem was discretized into the limit of a series of Lagrange interpolation problems. When the interpolation condition of  Hermite-type interpolation  problem corresponded to a second-order D-invariant subspace,  a necessary and sufficient  condition for the problem to be discretized under the idea of discrete approximation algorithm was given by using the structural property of the space. The nonlinear  equations corresponding to the  condition were smaller in scale and more efficient in computation.