Related papers: The GSVD: Where are the ellipses?, Matrix Trigonom…
A sufficient condition for the existence of a solution for generalized vector equilibrium problem (GVEP) on Hadamard manifold, by using a version of KKM lemma on this context, is presented in this paper. It is worth to point out that, in…
This article focuses on solving the generalized eigenvalue problems (GEP) arising in the source-free Maxwell equation with magnetoelectric coupling effects that models three-dimensional complex media. The goal is to compute the smallest…
This work develops a multiscale solution decomposition (MSD) method for nonlocal-in-time problems to separate a series of known terms with multiscale singularity from the original singular solution such that the remaining unknown part…
Within the theory of General Relativity, we study the solution and range of applicability of the standard geodesic deviation equation in highly symmetric spacetimes. In the Schwarzschild spacetime, the solution is used to model satellite…
Assuming the four-dimensional space-time to be a general warped product of two surfaces we reduce the four-dimensional Einstein equations to a two-dimensional problem which can be solved. All global vacuum solutions are explicitly…
Under certain conditions, an element of a tensor product space can be identified with a compact operator and the singular value decomposition (SVD) applies to the latter. These conditions are not fulfilled in Sobolev spaces. In the previous…
This paper is a self-contained presentation of certain aspects of the theory of weighted Sobolev spaces and elliptic operators on non-compact Riemannian manifolds. Specifically, we discuss (i) the standard and weighted Sobolev Embedding…
We build a solvability theory of elliptic boundary-value problems in normed Sobolev spaces of generalized smoothness for any integrability exponent $p>1$. The smoothness is given by a number parameter and a supplementary function parameter…
Stochastic differential equations are ubiquitous modelling tools in physics and the sciences. In most modelling scenarios, random fluctuations driving dynamics or motion have some non-trivial temporal correlation structure, which renders…
Sparsity regularization has garnered significant interest across multiple disciplines, including statistics, imaging, and signal processing. Standard techniques for addressing sparsity regularization include iterative soft thresholding…
We introduce the Graph Sylvester Embedding (GSE), an unsupervised graph representation of local similarity, connectivity, and global structure. GSE uses the solution of the Sylvester equation to capture both network structure and…
Singular Value Decomposition (SVD) is one of the most useful techniques for analyzing data in linear algebra. SVD decomposes a rectangular real or complex matrix into two orthogonal matrices and one diagonal matrix. In this work we…
We study the task of clustering in directed networks. We show that using the eigenvalue/eigenvector decomposition of the adjacency matrix is simpler than all common methods which are based on a combination of data regularization and SVD…
We introduce a new approach for robotic manipulation tasks in human settings that necessitates understanding the 3D geometric connections between a pair of objects. Conventional end-to-end training approaches, which convert pixel…
The goal of this paper is to define the Grassmann integral in terms of a limit of a sum around a well-defined contour so that Grassmann numbers gain geometric meaning rather than symbols. The unusual rescaling properties of the integration…
We develop the theory of a generalized probability tomography method to image source poles and dipoles of a geophysical vector or scalar field dataset. The purpose of the new generalized method is to improve the resolution power of buried…
Quantum-inspired singular value decomposition (SVD) is a technique to perform SVD in logarithmic time with respect to the dimension of a matrix, given access to the matrix embedded in a segment-tree data structure. The speedup is possible…
In his book on Convex Polyhedra (section 7.2), A.D. Aleksandrov raised a general question of finding variational statements and proofs of existence of polytopes with given geometric data. The first goal of this paper is to give a…
Singular value decomposition (SVD) is a standard matrix factorization technique that produces optimal low-rank approximations of matrices. It has diverse applications, including machine learning, data science and signal processing. However,…
Finding constrained saddle points on Riemannian manifolds is significant for analyzing energy landscapes arising in physics and chemistry. Existing works have been limited to special manifolds that admit global regular level-set…