On a C. de Boor's Conjecture in a Particular Case and Related Perturbation

Details On a C. de Boor's Conjecture in a Particular Case and Related Perturbation On a C. de Boor's Conjecture in a Particular Case and Related Perturbation

2011-02-15

arxiv.org/abs/1102.3201v1

Mathematics

Numerical Analysis

Scientific paper

In this paper, we focus on two classes of D-invariant polynomial subspaces. The first is a classical type, while the second is a new class. With matrix computation, we prove that every ideal projector with each D-invariant subspace belonging to either the first class or the second is the pointwise limit of Lagrange projectors. This verifies a particular case of a C. de Boor's conjecture asserting that every complex ideal projector is the pointwise limit of Lagrange projectors. Specifically, we provide the concrete perturbation procedure for ideal projectors of this type.

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