相关论文: Computing Individual Discrete Logarithms Faster in…

Solving partial differential equations (PDEs) on manifolds defined by randomly sampled point clouds is a challenging problem in scientific computing and has broad applications in various fields. In this paper, we develop a two-step…

We consider the problem of estimating log-determinants of large, sparse, positive definite matrices. A key focus of our algorithm is to reduce computational cost, and it is based on sparse approximate inverses. The algorithm can be…

In this paper we discuss the problem of performing elementary finite field arithmetic on a quantum computer. Of particular interest, is the controlled-multiplication operation, which is the only group-specific operation in Shor's algorithms…

Nonnegative matrix factorization (NMF) often relies on the separability condition for tractable algorithm design. Separability-based NMF is mainly handled by two types of approaches, namely, greedy pursuit and convex programming. A notable…

We consider a generic framework of optimization algorithms based on gradient descent. We develop a quantum algorithm that computes the gradient of a multi-variate real-valued function $f:\mathbb{R}^d\rightarrow \mathbb{R}$ by evaluating it…

In this article, we study algorithms for nonnegative matrix factorization (NMF) in various applications involving streaming data. Utilizing the continual nature of the data, we develop a fast two-stage algorithm for highly efficient and…

In this paper, we study convex optimization methods for computing the trace norm regularized least squares estimate in multivariate linear regression. The so-called factor estimation and selection (FES) method, recently proposed by Yuan et…

We revisit the reduction of Cheng and Wan, which transforms instances of the discrete logarithm problem (DLOG) over finite fields into a decoding problem for Reed--Solomon codes, and study how Regev's reduction can be used to solve these…

Natural language processing (NLP) sees rich mobile applications. To support various language understanding tasks, a foundation NLP model is often fine-tuned in a federated, privacy-preserving setting (FL). This process currently relies on…

We develop a mesh-free, derivative-free, matrix-free, and highly parallel localized stochastic method for high-dimensional semilinear parabolic PDEs. The efficiency of the proposed method is built upon four essential components: (i) a…

We present an algorithm for computing discriminants and prime ideal decomposition in number fields. The algorithm is a refinement of a p-adic factorization method based on Newton polygons of higher order. The running-time and memory…

The Multilevel Fast Multipole Algorithm (MLFMA) has known applications in scientific modeling in the fields of telecommunications, physics, mechanics, and chemistry. Accelerating calculation of far-field using GPUs and GPU clusters for…

It is well known that Newton's method can have trouble converging if the initial guess is too far from the solution. Such a problem particularly occurs when this method is used to solve nonlinear elliptic partial differential equations…

Applications in quantitative finance such as optimal trade execution, risk management of options, and optimal asset allocation involve the solution of high dimensional and nonlinear Partial Differential Equations (PDEs). The connection…

We propose to use Digital Memcomputing Machines (DMMs), implemented with self-organizing logic gates (SOLGs), to solve the problem of numerical inversion. Starting from fixed-point scalar inversion we describe the generalization to solving…

Differential Privacy (DP) provides a formal framework for training machine learning models with individual example level privacy. In the field of deep learning, Differentially Private Stochastic Gradient Descent (DP-SGD) has emerged as a…

Machine-learning systems continue to advance at a rapid pace, demonstrating remarkable utility in various fields and disciplines. As these systems continue to grow in size and complexity, a nascent industry is emerging which aims to bring…

Deep neural network models can be used to learn complex dynamics from data and reconstruct sparse or noisy signals, thereby accelerating and augmenting experimental measurements. Evaluating the quantum optical properties of solid-state…

Non-negative least squares (NNLS) problem is one of the most important fundamental problems in numeric analysis. It has been widely used in scientific computation and data modeling. In big data, the limitations of algorithm speed and…

We examine what is an efficient and scalable nonlinear solver, with low work and memory complexity, for many classes of discretized partial differential equations (PDEs) - matrix-free Full multigrid (FMG) with a Full Approximation Storage…