ideal interpolation
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Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 193
Author(s):  
Xue Jiang ◽  
Kai Cui

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







2016 ◽  
Vol 308 ◽  
pp. 177-186
Author(s):  
Xue Jiang ◽  
Shugong Zhang ◽  
Baoxin Shang
Keyword(s):  




2016 ◽  
Vol 148 (2) ◽  
pp. 466-480 ◽  
Author(s):  
Y. H. Gong ◽  
X. Jiang ◽  
Z. Li ◽  
S. G. Zhang


2010 ◽  
Vol 162 (7) ◽  
pp. 1398-1406 ◽  
Author(s):  
Boris Shekhtman






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