The Representation of D-Invariant Polynomial Subspaces Based on Symmetric Cartesian Tensors

نویسندگان

چکیده

Multivariate polynomial interpolation plays a crucial role both in scientific computation and engineering application. Exploring the structure of D-invariant (closed under differentiation) subspaces has significant meaning for multivariate Hermite-type (especially ideal interpolation). We analyze subspace Pn terms Cartesian tensors, where is with maximal total degree equal to n,n≥1. For an arbitrary homogeneous p(k) k Pn, can be rewritten as inner products kth order symmetric tensor column vectors indeterminates. show that determined by all polynomials one Pn. Namely, if we treat linear on basis vector, then this vector written product coefficient matrix A(1) indeterminates; our main result shows corresponds some so-called relational matrices A(1).

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ژورنال

عنوان ژورنال: Axioms

سال: 2021

ISSN: ['2075-1680']

DOI: https://doi.org/10.3390/axioms10030193