相关论文: Properties of the solution set of generalized poly…
By using the squared slack variables technique, we demonstrate that the solution set of a general polynomial complementarity problem is the image, under a specific projection, of the set of real zeroes of a system of polynomials. This paper…
CP decomposition is a powerful tool for data science, especially gene analysis, deep learning, and quantum computation. However, the application of tensor decomposition is largely hindered by the exponential increment of the computational…
Missing entries in multi dimensional data pose significant challenges for downstream analysis across diverse real world applications. These data are naturally represented as tensors, and recent completion methods integrating global low rank…
We consider the Klein-Gordon and sine-Gordon type equations with a point-like potential, which describes the wave phenomenon in disordered media with a defect. The singular potential term yields a critical phenomenon--that is, the solution…
It is important for performance studies in quantum technologies to analyze quantum circuits in the presence of noise. We introduce an error probability tensor, a tool to track generalized Pauli error statistics of qudits within quantum…
In this paper, we study the stochastic linear complementarity problems on extended second order cones (stochastic ESOCLCP). We first convert the problem to a stochastic mixed complementarity problem on the nonegative orthant (SMixCP).…
A subset $S$ of vertices of a graph $G$ is called a perfectly matchable set of $G$ if the subgraph induced by $S$ contains a perfect matching. The perfectly matchable set polynomial of $G$, first made explicit by Ohsugi and Tsuchiya, is the…
We present new alternative complete asymptotic expansions for the time harmonic low--frequency magnetic field perturbation caused by the presence of a conducting permeable object as its size tends to zero for the eddy current approximation…
In the total matching problem, one is given a graph $G$ with weights on the vertices and edges. The goal is to find a maximum weight set of vertices and edges that is the non-incident union of a stable set and a matching. We consider the…
The breakthrough paper of Croot, Lev, Pach \cite{CLP} on progression-free sets in $\Z_4^n$ introduced a polynomial method that has generated a wealth of applications, such as Ellenberg and Gijswijt's solutions to the cap set problem…
We first extend the construction of generalized barycentric coordinates (GBC) based on the vertices on the boundary of a polygon $\Omega$ to a new kind of GBCs based on vertices inside the $\Omega$ of interest. For clarity, the standard…
We investigate a novel approach to approximate tensor-network contraction via the exact, matrix-free decomposition of full tensor-networks. We study this method as a means to eliminate the propagation of error in the approximation of…
We study rigidity/flexibility properties of global solutions to the thin obstacle problem. For solutions with bounded positive sets, we give a classification in terms of their expansions at infinity. For solutions with bounded contact sets,…
We are interested in finding a solution to the tensor complementarity problem with a strong M-tensor, which we call the M-tensor complementarity problem. We propose a lower dimensional linear equation approach to solve that problem. At each…
A pair $(C, D)$ of group codes over group algebra $R[G]$ is called a linear complementary pair (LCP) if $C \oplus D =R[G]$, where $R$ is a finite principal ideal ring, and $G$ is a finite group. We provide a necessary and sufficient…
We study decay and compact support properties of positive and bounded solutions of $\Delta_{p} u \geq \Lambda(u)$ on the exterior of a compact set of a complete manifold with rotationally symmetry. In the same setting, we also give a new…
This paper studies symmetric tensor decompositions. For symmetric tensors, there exist linear relations of recursive patterns among their entries. Such a relation can be represented by a polynomial, which is called a generating polynomial.…
In view of the KS-tensor complementarity problem, the sparse solution of this problem is studied. Due to the nonconvexity and noncontinuity of the l_0-norm, it is a NP hard problem to find the sparse solution of the KS-tensor…
Although a unique solution is guaranteed in the Linear complementarity problem (LCP) when the matrix $\mathbf{M}$ is positive definite, practical applications often involve cases where $\mathbf{M}$ is only positive semi-definite, leading to…
Canonical polyadic decomposition (CPD) is at the core of fast matrix multiplication, a computational problem with widespread implications across several seemingly unrelated problems in computer science. Much recent progress in this field…