Abstract: 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.

Key words: multivariate Hermite-type interpolation, Lagrange interpolation, discretization, second-order D-invariant subspace