相关论文: Zolotarev Quadrature Rules and Load Balancing for …
A searcher is tasked with exploring a graph with edge lengths and vertex weights, starting from a designated vertex. Initially, only the starting vertex is considered explored. At each step, the searcher adds an edge to the solution,…
Iterative algorithms based on thresholding, feedback and null space tuning (NST+HT+FB) for sparse signal recovery are exceedingly effective and fast, particularly for large scale problems. The core algorithm is shown to converge in finitely…
Randomized linear system solvers have become popular as they have the potential to reduce floating point complexity while still achieving desirable convergence rates. One particularly promising class of methods, random sketching solvers,…
We develop a generalization of Nesterov's accelerated gradient descent method which is designed to deal with orthogonality constraints. To demonstrate the effectiveness of our method, we perform numerical experiments which demonstrate that…
A fundamental class of matrix optimization problems that arise in many areas of science and engineering is that of quadratic optimization with orthogonality constraints. Such problems can be solved using line-search methods on the Stiefel…
In this work, we study the problem of finding approximate, with minimum support set, solutions to matrix max-plus equations, which we call sparse approximate solutions. We show how one can obtain such solutions efficiently and in polynomial…
One of the most popular and important first-order iterations that provides optimal complexity of the classical proximal gradient method (PGM) is the "Fast Iterative Shrinkage/Thresholding Algorithm" (FISTA). In this paper, two inexact…
The parallel full approximation scheme in space and time (PFASST) introduced by Emmett and Minion in 2012 is an iterative strategy for the temporal parallelization of ODEs and discretized PDEs. As the name suggests, PFASST is similar in…
We present a novel deep learning approach to approximate the solution of large, sparse, symmetric, positive-definite linear systems of equations. These systems arise from many problems in applied science, e.g., in numerical methods for…
In this paper we study constrained subspace approximation problem. Given a set of $n$ points $\{a_1,\ldots,a_n\}$ in $\mathbb{R}^d$, the goal of the {\em subspace approximation} problem is to find a $k$ dimensional subspace that best…
Self-similarity techniques are booming in blind super-resolution (SR) due to accurate estimation of the degradation types involved in low-resolution images. However, high-dimensional matrix multiplication within self-similarity computation…
We develop a new spatial semidiscrete multiscale method based upon the edge multiscale methods to solve semilinear parabolic problems with heterogeneous coefficients and smooth initial data. This method allows for a cheap spatial…
The aim of this paper is to propose an efficient adaptive finite element method for eigenvalue problems based on the multilevel correction scheme and inverse power method. This method involves solving associated boundary value problems on…
Parameter-efficient finetuning (PEFT) methods seek to adapt large neural models via updates to a small number of weights. However, much prior interpretability work has shown that representations encode rich semantic information, suggesting…
Subspace clustering methods based on $\ell_1$, $\ell_2$ or nuclear norm regularization have become very popular due to their simplicity, theoretical guarantees and empirical success. However, the choice of the regularizer can greatly impact…
In the era of the James Webb Space Telescope (JWST), the dramatic improvement in the spectra of exoplanetary atmospheres demands a corresponding leap forward in our ability to analyze them: atmospheric retrievals need to be performed on…
We describe an efficient method for the approximation of functions using radial basis functions (RBFs), and extend this to a solver for boundary value problems on irregular domains. The method is based on RBFs with centers on a regular grid…
The numerical integration of stiff equations is a challenging problem that needs to be approached by specialized numerical methods. Exponential integrators form a popular class of such methods since they are provably robust to stiffness and…
Many modern big data applications feature large scale in both numbers of responses and predictors. Better statistical efficiency and scientific insights can be enabled by understanding the large-scale response-predictor association network…
Parameter-Efficient Fine-Tuning (PEFT) methods have gained significant popularity for adapting pre-trained Large Language Models (LLMs) to downstream tasks, primarily due to their potential to significantly reduce memory and computational…