English
Related papers

Related papers: Orthogononalization on a general purpose graphics …

200 papers

Many quantum algorithms for attacking symmetric cryptography involve the rank problem of quantum linear equations. In this paper, we first propose two quantum algorithms for solving quantum linear systems of equations with coherent…

Quantum Physics · Physics 2024-05-14 Qiqing Xia , Qianru Zhu , Huiqin Xie , Li Yang

In this paper, we accomplish a unified convergence analysis of a second-order method of multipliers (i.e., a second-order augmented Lagrangian method) for solving the conventional nonlinear conic optimization problems.Specifically, the…

Optimization and Control · Mathematics 2021-10-01 Liang Chen , Junyuan Zhu , Xinyuan Zhao

This paper is concerned with the convergence of a two-step modified Newton method for solving the nonlinear system arising from the minimal nonnegative solution of nonsymmetric algebraic Riccati equations from neutron transport theory. We…

Numerical Analysis · Mathematics 2025-07-22 Juan Liang , Yonghui Ling

We present iterative solvers to approximate the solution of numerical schemes for stochastic Stefan problems. After briefly talking about the convergence results, we tackle the question of efficient strategies for solving the nonlinear…

Numerical Analysis · Mathematics 2025-08-12 Muhammad Awais Khan , Jérôme Droniou , Kim-Ngan Le , Iuliu Sorin Pop

We are interested in solving linear systems arising from three applications: (1) kernel methods in machine learning, (2) discretization of boundary integral equations from mathematical physics, and (3) Schur complements formed in the…

Numerical Analysis · Mathematics 2022-08-15 Chao Chen , Per-Gunnar Martinsson

Large scale graph optimization problems arise in many fields. This paper presents an extensible, high performance framework (named OpenGraphGym-MG) that uses deep reinforcement learning and graph embedding to solve large graph optimization…

Distributed, Parallel, and Cluster Computing · Computer Science 2021-06-25 Weijian Zheng , Dali Wang , Fengguang Song

Feedforward computation, such as evaluating a neural network or sampling from an autoregressive model, is ubiquitous in machine learning. The sequential nature of feedforward computation, however, requires a strict order of execution and…

Machine Learning · Computer Science 2021-06-15 Yang Song , Chenlin Meng , Renjie Liao , Stefano Ermon

This work introduces a new approach for accelerating the numerical analysis of time-domain partial differential equations (PDEs) governing complex physical systems. The methodology is based on a combination of a classical reduced-order…

Machine Learning · Computer Science 2024-06-06 Victor Matray , Faisal Amlani , Frédéric Feyel , David Néron

Kernel methods for solving partial differential equations on surfaces have the advantage that those methods work intrinsically on the surface and yield high approximation rates if the solution to the partial differential equation is smooth…

Numerical Analysis · Mathematics 2024-10-04 Thomas Hangelbroek , Christian Rieger

The problem of minimizing a sum of local convex objective functions over a networked system captures many important applications and has received much attention in the distributed optimization field. Most of existing work focuses on…

Optimization and Control · Mathematics 2019-01-09 Fatemeh Mansoori , Ermin Wei

The Newton, Gauss--Newton and Levenberg--Marquardt methods all use the first derivative of a vector function (the Jacobian) to minimise its sum of squares. When the Jacobian matrix is ill-conditioned, the function varies much faster in some…

Numerical Analysis · Mathematics 2025-08-01 S. J. Brooks

The complexity of black-box algorithms can lead to various challenges, including the introduction of biases. These biases present immediate risks in the algorithms' application. It was, for instance, shown that neural networks can deduce…

Machine Learning · Computer Science 2024-06-04 David Rügamer , Chris Kolb , Tobias Weber , Lucas Kook , Thomas Nagler

In this paper, we propose an inexact perturbed path-following algorithm in the framework of Lagrangian dual decomposition for solving large-scale structured convex optimization problems. Unlike the exact versions considered in literature,…

Optimization and Control · Mathematics 2011-09-16 Quoc Tran Dinh , Ion Necoara , Carlo Savorgnan , Moritz Diehl

Bilinear pooling of Convolutional Neural Network (CNN) features [22, 23], and their compact variants [10], have been shown to be effective at fine-grained recognition, scene categorization, texture recognition, and visual question-answering…

Computer Vision and Pattern Recognition · Computer Science 2017-07-24 Tsung-Yu Lin , Subhransu Maji

Here we present an implementation of Primal-Dual Affine scaling method to solve linear optimization problem on GPU based systems. Strategies to convert the system generated by complementary slackness theorem into a symmetric system are…

Numerical Analysis · Computer Science 2015-02-13 Nithish Divakar

Multigrid methods have been a popular approach for solving linear systems arising from the discretization of partial differential equations (PDEs) for several decades. They are particularly effective for accelerating convergence rates with…

Numerical Analysis · Mathematics 2025-12-10 Teoman Toprak , Florian Kummer

In this paper, we propose a globally convergent Newton type method to solve $\ell_0$ regularized sparse optimization problem. In fact, a line search strategy is applied to the Newton method to obtain global convergence. The Jacobian matrix…

Optimization and Control · Mathematics 2025-11-26 Yuge Ye , Qingna Li

We consider regular polynomial interpolation algorithms on recursively defined sets of interpolation points which approximate global solutions of arbitrary well-posed systems of linear partial differential equations. Convergence of the…

Numerical Analysis · Mathematics 2008-07-10 Joerg Kampen

In this paper we consider a family of algorithms for approximate implicitization of rational parametric curves and surfaces. The main approximation tool in all of the approaches is the singular value decomposition, and they are therefore…

Numerical Analysis · Mathematics 2016-05-30 Oliver J. D. Barrowclough , Tor Dokken

This paper studies deep neural networks for solving extremely large linear systems arising from highdimensional problems. Because of the curse of dimensionality, it is expensive to store both the solution and right-hand side vector in such…

Numerical Analysis · Mathematics 2023-03-07 Yiqi Gu , Michael K. Ng