Properly posed sets of nodes for multivariate lagrange interpolation in C-s

摘要

In this paper, we apply techniques from the theory of ideals and varieties in algebraic geometry to study the geometric structure of a properly posed set of nodes (or PPSN, for short) for multivariate Lagrange interpolation along an algebraic hypersurface. We provide a hyperplane-superposition process to construct the PPSN for interpolation along an algebraic hypersurface, and as a result, we offer a clear understanding of the geometric structure of the PPSN for multivariate Lagrange interpolation in C-s. [References: 10]