scholarly journals Ideal interpolation: Mourrain's condition vs. D-invariance

2006 ◽  
Author(s):  
C. de Boor
Keyword(s):  
Ideal Interpolation

scholarly journals Error formulas for ideal interpolation

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

scholarly journals On the Ideal Interpolation Operator in Algebraic Multigrid Methods

2018 ◽  
Vol 56 (3) ◽  
pp. 1693-1710 ◽  
Author(s):  
Xuefeng Xu ◽  
Chen-Song Zhang
Keyword(s):  
Multigrid Methods ◽  
Algebraic Multigrid ◽  
Interpolation Operator ◽  
Ideal Interpolation ◽  
Algebraic Multigrid Methods ◽  
The Ideal

scholarly journals On a conjecture of Tomas Sauer regarding nested ideal interpolation

2008 ◽  
Vol 137 (05) ◽  
pp. 1723-1728 ◽  
Author(s):  
Boris Shekhtman
Keyword(s):  
Ideal Interpolation

scholarly journals The structure of a second-degree D-invariant subspace and its application in ideal interpolation

2016 ◽  
Vol 207 ◽  
pp. 232-240 ◽  
Author(s):  
Xue Jiang ◽  
Shugong Zhang
Keyword(s):  
Invariant Subspace ◽  
Ideal Interpolation ◽  
Second Degree

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

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 193
Author(s):  
Xue Jiang ◽  
Kai Cui
Keyword(s):  
Polynomial Interpolation ◽  
Engineering Application ◽  
Coefficient Matrix ◽  
Column Vector ◽  
Invariant Polynomial ◽  
Total Degree ◽  
Multivariate Polynomial ◽  
Multivariate Polynomial Interpolation ◽  
Treat All ◽  
Ideal Interpolation

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).

scholarly journals The discretization for bivariate ideal interpolation

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

Unbiased timing error estimation in the presence of non-ideal interpolation

2002 ◽  
Author(s):  
D. Kim ◽  
M.J. Narasimha ◽  
D.C. Cox
Keyword(s):  
Error Estimation ◽  
Timing Error ◽  
Ideal Interpolation

The effect of non-ideal interpolation on symbol synchronizer performance

1995 ◽  
Vol 6 (6) ◽  
pp. 627-632 ◽  
Author(s):  
Katrien Bucket ◽  
Marc Moeneclaey
Keyword(s):  
Ideal Interpolation
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