Related papers: Uniqueness Analysis of Non-Unitary Matrix Joint Di…

This paper introduces a polynomial blind algorithm that determines when two square matrices, $A$ and $B$, are permutation similar. The shifted and translated matrices $(A+\beta I+\gamma J)$ and $(B+\beta I+\gamma J)$ are used to color the…

This paper studies the numerical solution of traveling singular sources problems. In such problems, a big challenge is the sources move with different speeds, which are described by some ordinary differential equations. A…

In this work, we consider the problem of blind source separation (BSS) by departing from the usual linear model and focusing on the linear-quadratic (LQ) model. We propose two provably robust and computationally tractable algorithms to…

We prove existence, uniqueness and regularity results for mixed boundary value problems associated with fully nonlinear, possibly singular or degenerate elliptic equations. Our main result is a global H\"older estimate for solutions,…

We introduce a generalization of the linearized Alternating Direction Method of Multipliers to optimize a real-valued function $f$ of multiple arguments with potentially multiple constraints $g_\circ$ on each of them. The function $f$ may…

We consider geometric multigrid methods for the solution of linear systems arising from isogeometric discretizations of elliptic partial differential equations. For classical finite elements, such methods are well known to be fast solvers…

This paper has made some significant advances in the boundary-only and domain-type RBF techniques. The proposed boundary knot method (BKM) is different from the standard boundary element method in a number of important aspects. Namely, it…

In this paper, we propose a novel and efficient CNN-based framework that leverages local and global context information for image denoising. Due to the limitations of convolution itself, the CNN-based method is generally unable to construct…

An algorithm is developed to compute the complete CS decomposition (CSD) of a partitioned unitary matrix. Although the existence of the CSD has been recognized since 1977, prior algorithms compute only a reduced version (the 2-by-1 CSD)…

Graphs are very important mathematical structures used in many applications, one of which is transportation science. When dealing with transportation networks, one deals not only with the network structure, but also with information related…

Matrix factorizations in dual number algebra, a hypercomplex system, have been applied to kinematics, mechanisms, and other fields recently. We develop an approach to identify spatiotemporal patterns in the brain such as traveling waves…

The Deligne-Simpson problem (DSP) (resp. the weak DSP) is formulated like this: {\em give necessary and sufficient conditions for the choice of the conjugacy classes $C_j\subset GL(n,{\bf C})$ or $c_j\subset gl(n,{\bf C})$ so that there…

In this paper we study higher-order difference equations which can be written as follows: $$ \mathbf{J} (y_0,y_1,...)^T = \lambda^N (y_0,y_1,...)^T, $$ where $\mathbf{J}$ is a $(2N+1)$-diagonal bounded banded matrix…

This paper develops matrix-multiplication-based iterative refinement for diagonalizable non-Hermitian eigendecompositions. The main theory concerns simple eigenvalues and distinguishes two input regimes. In the right-only regime, where only…

This paper provides a direct method of establishing the existence and uniqueness of saddle-node bifurcations for nonlinear equations in general domains. The method employs the scaled extended quotient whose saddle points correspond to the…

A general method to generate a centrosymmetric matrix associated with the solving of partial differential equation (PDE) on an irreducible domain by means of a linear equation system is proposed. The method applies to any PDE for which both…

Matrix Factorization is a popular non-convex optimization problem, for which alternating minimization schemes are mostly used. They usually suffer from the major drawback that the solution is biased towards one of the optimization…

In this paper, we introduce a powerful technique based on Leave-one-out analysis to the study of low-rank matrix completion problems. Using this technique, we develop a general approach for obtaining fine-grained, entrywise bounds for…

This work investigates conditions for quantitative image reconstruction in multispectral computed tomography (MSCT), which remains a topic of active research. In MSCT, one seeks to obtain from data the spatial distribution of linear…

This paper focuses on the problem of localising a transmitting mobile station (MS) using multiple cooperative base stations (BSs). There are two technical difficulties: one is the data association between intermediate parameters and…