Related papers: Dissecting the FEAST algorithm for generalized eig…
When a feed-forward neural network (FNN) is trained for source ranging in an ocean waveguide, it is difficult evaluating the range accuracy of the FNN on unlabeled test data. A fitting-based early stopping (FEAST) method is introduced to…
A new approach to solving eigenvalue optimization problems for large structured matrices is proposed and studied. The class of optimization problems considered is related to computing structured pseudospectra and their extremal points, and…
The large models, as predicted by scaling raw forecasts, have made groundbreaking progress in many fields, particularly in natural language generation tasks, where they have approached or even surpassed human levels. However, the…
In this article, we present two new greedy algorithms for the computation of the lowest eigenvalue (and an associated eigenvector) of a high-dimensional eigenvalue problem, and prove some convergence results for these algorithms and their…
We consider the approximation of elliptic eigenvalue problem with an immersed interface. The main aim of this paper is to prove the stability and convergence of an immersed finite element method (IFEM) for eigenvalues using Crouzeix-Raviart…
Large-scale optimization problems that seek sparse solutions have become ubiquitous. They are routinely solved with various specialized first-order methods. Although such methods are often fast, they usually struggle with not-so-well…
The study of fractional order differential operators is receiving renewed attention in many scientific fields. In order to accommodate researchers doing work in these areas, there is a need for highly scalable numerical methods for solving…
In this paper, we present a novel parallel augmented subspace method and build a package Parallel Augmented Subspace Eigensolver (PASE) for solving large scale eigenvalue problems by the massively parallel finite element discretization.…
We propose a new method to solve eigenvalue problems for linear and semilinear second order differential operators in high dimensions based on deep neural networks. The eigenvalue problem is reformulated as a fixed point problem of the…
A generalized finite element method is proposed for solving a heterogeneous reaction-diffusion equation with a singular perturbation parameter $\varepsilon$, based on locally approximating the solution on each subdomain by solution of a…
Despite being a key bottleneck in many machine learning tasks, the cost of solving large linear systems has proven challenging to quantify due to problem-dependent quantities such as condition numbers. To tackle this, we consider a…
Random Fourier Features (RFF) is among the most popular and broadly applicable approaches for scaling up kernel methods. In essence, RFF allows the user to avoid costly computations on a large kernel matrix via a fast randomized…
One of the main computational bottlenecks when working with kernel based learning is dealing with the large and typically dense kernel matrix. Techniques dealing with fast approximations of the matrix vector product for these kernel…
Many problems in science and engineering involve, as part of their solution process, the consideration of a separable function which is the sum of two convex functions, one of them possibly non-smooth. Recently a few works have discussed…
It is well-known that the finite difference discretization of the Laplacian eigenvalue problem $-\Delta u = \lambda u$ leads to a matrix eigenvalue problem (EVP) $A x= \lambda x$ where the matrix $A$ is Toeplitz-plus-Hankel. Analytical…
In order to guarantee the downloading quality requirements of users and improve the stability of data transmission in a BitTorrent-like peer-to-peer file sharing system, this article deals with eigenproblems of addition-min algebras. First,…
Computing the similarity between two protein structures is a crucial task in molecular biology, and has been extensively investigated. Many protein structure comparison methods can be modeled as maximum clique problems in specific k-partite…
We propose a flexible machine-learning framework for solving eigenvalue problems of diffusion operators in moderately large dimension. We improve on existing Neural Networks (NNs) eigensolvers by demonstrating our approach ability to…
The rise of deep learning has marked significant progress in fields such as computer vision, natural language processing, and medical imaging, primarily through the adaptation of pre-trained models for specific tasks. Traditional…
Motivated by applications such as sparse PCA, in this paper we present provably-accurate one-pass algorithms for the sparse approximation of the top eigenvectors of extremely massive matrices based on a single compact linear sketch. The…