Abstract
In this article, Lagrange interpolation by polynomials in several variables is studied in a systematic way. After defining properly posed set of nodes (PPSN) along the sufficiently intersected algebraic manifolds, we give the sufficient and necessary condition for judging PPSN and propose the generally constructive method of PPSN for Lagrange interpolation along algebraic manifolds, which is named as an algebraic hypersurface-superposition process. The theory is illustrated with a simple example in ℝ3. Moreover, the relationship between the sufficiently intersected polynomials and H-basis is also discussed.
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