相关论文: Singular Value Decompositions for Single-Curl Oper…

For arbitrarily small values of $\varepsilon>0,$ we formulate and analyse the Maxwell system of equations of electromagnetism on $\varepsilon$-periodic sets $S^\varepsilon\subset{\mathbb R}^3.$ Assuming that a family of Borel measures…

We introduce a new family of discontinuous Galerkin (DG) finite element schemes for the discretization of first order systems of hyperbolic partial differential equations (PDE) on unstructured simplex meshes in two and three space…

In this paper we introduce the algorithm and the fixed point hardware to calculate the normalized singular value decomposition of a non-symmetric matrices using Givens fast (approximate) rotations. This algorithm only uses the basic…

Building on the abstract Generalized Singular Value Decomposition (GSVD) theory of Brown et al. [2025], we prove that most modern neural architectures admit a generalized SVD representation in which they are left-invertible before a final…

The spectral transformation Lanczos method for the sparse symmetric definite generalized eigenvalue problem for matrices $A$ and $B$ is an iterative method that addresses the case of semidefinite or ill conditioned $B$ using a shifted and…

Finite element methods for electromagnetic problems modeled by Maxwell-type equations are highly sensitive to the conformity of approximation spaces, and non-conforming methods may cause loss of convergence. This fact leads to an essential…

The signal resulting from magnetic resonance spectroscopy is occupied by noises and irregularities so in the further analysis preprocessing techniques have to be introduced. The main idea of the paper is to develop a model of a signal as a…

In this paper we propose an accurate, highly parallel algorithm for the generalized eigendecomposition of a matrix pair $(H, S)$, given in a factored form $(F^{\ast} J F, G^{\ast} G)$. Matrices $H$ and $S$ are generally complex and…

Our goal is to efficiently compute low-dimensional latent coordinates for nodes in an input graph -- known as graph embedding -- for subsequent data processing such as clustering. Focusing on finite graphs that are interpreted as uniform…

This paper concerns the preconditioning technique for discrete systems arising from time-harmonic Maxwell equations with absorptions, where the discrete systems are generated by N\'ed\'elec finite element methods of fixed order on meshes…

Singular Value Decomposition (SVD) is a fundamental matrix factorization technique in linear algebra, widely applied in numerous matrix-related problems. However, traditional SVD approaches are hindered by slow panel factorization and…

In this paper, we propose a general method to obtain a set of Linearly Independent Non-Orthogonal yet Energy (square of the norm) Preserving (LINOEP) vectors using iterative filtering operation and we refer it as Filter Mode Decomposition…

In [Camano, Lackner, Monk, SIAM J. Math. Anal., Vol. 49, No. 6, pp. 4376-4401 (2017)] it was suggested to use Stekloff eigenvalues for Maxwell equations as target signature for nondestructive testing via inverse scattering. The authors…

Full waveform inversion (FWI) is a large-scale nonlinear ill-posed problem for which computationally expensive Newton-type methods can become trapped in undesirable local minima, particularly when the initial model lacks a low-wavenumber…

Objective: Global Maxwell Tomography (GMT) is a noninvasive inverse optimization method for the estimation of electrical properties (EP) from magnetic resonance (MR) measurements. GMT uses the volume integral equation (VIE) in the forward…

We have developed a new fully anisotropic 3D FDTD Maxwell solver for arbitrary electrically and magnetically anisotropic media for piecewise constant electric and magnetic materials that are co-located over the primary computational cells.…

Learning the principal eigenfunctions of an integral operator defined by a kernel and a data distribution is at the core of many machine learning problems. Traditional nonparametric solutions based on the Nystr{\"o}m formula suffer from…

In this paper, we propose a type of tensor-neural-network-based machine learning method to compute multi-eigenpairs of high dimensional eigenvalue problems without Monte-Carlo procedure. Solving multi-eigenvalues and their corresponding…

We develop an essentially optimal numerical method for solving multiscale Maxwell wave equations in a domain $D\subset{\mathbb R}^d$. The problems depend on $n+1$ scales: one macroscopic scale and $n$ microscopic scales. Solving the…

Pendry and MacKinnon meaningful discretization of Maxwell's equations was put forward specifically as part of a finite-element numerical algorithm. By contrast with a numerical approach, in the same spirit evoked by the relationships…