1 citations · 2 across the 8 of their papers we have counts for
8 papers
A New Result on Packing Unit Squares into a Large Square
Shuang Wang, Tian Dong, Jiamin Li
In their 2009 note: \emph{Packing equal squares into a large square}, Chung and Graham proved that the uncovered area of a large square of side length is $O\left(x^{(3+\sqrt{2}…
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…
Bivariate Quasi-Tower Sets and Their Associated Lagrange Interpolation Bases
Tian Dong, Xiaoying Wang, Shugong Zhang +1
As we all known, there is still a long way for us to solve arbitrary multivariate Lagrange interpolation in theory. Nevertheless, it is well accepted that theories about Lagrange i…
A Bivariate Preprocessing Paradigm for Buchberger-Möller Algorithm
Xiaoying Wang, Shugong Zhang, Tian Dong
For the last almost three decades, since the famous Buchberger-Möller(BM) algorithm emerged, there has been wide interest in vanishing ideals of points and associated interpolation…
A Two-Dimensional Improvement for Farr-Gao Algorithm
Tian Dong
Farr-Gao algorithm is a state-of-the-art algorithm for reduced Gröbner bases of vanishing ideals of finite points, which has been implemented in Maple as a build-in com…