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Fitzpatrick Algorithm for Multivariate Rational Interpolation
Peng Xia, Shugong Zhang, Na Lei
In this paper, we first apply the Fitzpatrick algorithm to osculatory rational interpolation. Then based on Fitzpatrick algorithm, we present a Neville-like algorithm for Cauchy in…
On a C. de Boor's Conjecture in a Particular Case and Related Perturbation
Zhe Li, Shugong Zhang, Tian Dong
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 e…
On existence of certain error formulas for a special class of ideal projectors
Zhe Li, Shugong Zhang, Tian Dong
In this paper, we focus on a special class of ideal projectors. With the aid of algebraic geometry, we prove that for this special class of ideal projectors, there exist "good" err…
Ideal Projectors of Type Partial Derivative and Their Perturbations
Zhe Li, Shugong Zhang, Tian Dong
In this paper, we verify Carl de Boor's conjecture on ideal projectors for real ideal projectors of type partial derivative by proving that there exists a positive $η\in \mathbb{R}…
Finite Sets of Affine Points with Unique Associated Monomial Order Quotient Bases
Zhe Li, Shugong Zhang, Tian Dong
The quotient bases for zero-dimensional ideals are often of interest in the investigation of multivariate polynomial interpolation, algebraic coding theory, and computational molec…