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In this paper we propose a method that uses Lagrange multipliers and numerical algebraic geometry to find all critical points, and therefore globally solve, polynomial optimization problems. We design a polyhedral homotopy algorithm that…

Optimization and Control · Mathematics 2023-02-10 Julia Lindberg , Leonid Monin , Kemal Rose

This paper presents the implementation of a HLLC finite volume solver using GPU technology for the solution of shallow water problems in two dimensions. It compares both CPU and GPU approaches for implementing all the solver's steps. The…

Computational Engineering, Finance, and Science · Computer Science 2018-07-03 Fabrice Zaoui

Numerical homotopy continuation methods for three classes of polynomial systems are presented. For a generic instance of the class, every path leads to a solution and the homotopy is optimal. The counting of the roots mirrors the resolution…

Numerical Analysis · Mathematics 2025-10-20 Jan Verschelde

Principal component analysis (PCA) is a key statistical technique for multivariate data analysis. For large data sets the common approach to PCA computation is based on the standard NIPALS-PCA algorithm, which unfortunately suffers from…

Quantitative Methods · Quantitative Biology 2008-11-10 M. Andrecut

The continually increasing volume of DNA sequence data has resulted in a growing demand for fast implementations of core algorithms. Computation of pairwise alignments between candidate haplotypes and sequencing reads using Pair-HMMs is a…

Distributed, Parallel, and Cluster Computing · Computer Science 2026-01-27 Bertil Schmidt , Felix Kallenborn , Alexander Wichmann , Alejandro Chacon , Christian Hundt

First-order methods based on the PDHG algorithm have recently emerged as a viable option for efficiently solving large-scale linear programming problems. One highly desirable property of these methods is that they can make effective use of…

Optimization and Control · Mathematics 2025-10-29 Edward Rothberg

Homotopy optimization is a traditional method to deal with a complicated optimization problem by solving a sequence of easy-to-hard surrogate subproblems. However, this method can be very sensitive to the continuation schedule design and…

Machine Learning · Computer Science 2023-07-25 Xi Lin , Zhiyuan Yang , Xiaoyuan Zhang , Qingfu Zhang

We introduce a fusion of GPU accelerated primal heuristics for Mixed Integer Programming. Leveraging GPU acceleration enables exploration of larger search regions and faster iterations. A GPU-accelerated PDLP serves as an approximate LP…

Optimization and Control · Mathematics 2025-10-31 Akif Çördük , Piotr Sielski , Alice Boucher , Kumar Aatish

The Guided Filter (GF) is well-known for its linear complexity. However, when filtering an image with an n-channel guidance, GF needs to invert an n x n matrix for each pixel. To the best of our knowledge existing matrix inverse algorithms…

Computer Vision and Pattern Recognition · Computer Science 2018-03-02 Longquan Dai , Mengke Yuan , Zechao Li , Xiaopeng Zhang , Jinhui Tang

Implicit methods and GPU parallelization are two distinct yet powerful strategies for accelerating high-order CFD algorithms. However, few studies have successfully integrated both approaches within high-speed flow solvers. The core…

Numerical Analysis · Mathematics 2025-09-09 Hongyu Liu , Xing Ji , Yuan Fu , Kun Xu

While the advances in synchrotron light sources, together with the development of focusing optics and detectors, allow nanoscale ptychographic imaging of materials and biological specimens, the corresponding experiments can yield…

Distributed, Parallel, and Cluster Computing · Computer Science 2022-04-05 Xiaodong Yu , Viktor Nikitin , Daniel J. Ching , Selin Aslan , Doga Gursoy , Tekin Bicer

We discuss in detail a recently proposed hybrid particle-continuum scheme for complex fluids and evaluate it at the example of a confined homopolymer solution in slit geometry. The hybrid scheme treats polymer chains near the impenetrable…

Soft Condensed Matter · Physics 2016-10-28 Shuanhu Qi , Hans Behringer , Thorsten Raasch , Friederike Schmid

This work presents a GPU-accelerated solver for the unit commitment (UC) problem in large-scale power grids. The solver uses the Primal-Dual Hybrid Gradient (PDHG) algorithm to efficiently solve the relaxed linear subproblem, achieving…

Optimization and Control · Mathematics 2025-12-09 Hussein Sharadga , Javad Mohammadi

This paper presents a Graphics Processing Units (GPUs) acceleration method of an iterative scheme for gas-kinetic model equations. Unlike the previous GPU parallelization of explicit kinetic schemes, this work features a fast converging…

Computational Physics · Physics 2020-01-08 Lianhua Zhu , Peng Wang , Songze Chen , Zhaoli Guo , Yonghao Zhang

Homogeneous diffusion inpainting can reconstruct missing image areas with high quality from a sparse subset of known pixels, provided that their location as well as their gray or color values are well optimized. This property is exploited…

Image and Video Processing · Electrical Eng. & Systems 2024-08-13 Niklas Kämper , Vassillen Chizhov , Joachim Weickert

In this work, we consider the solution of boundary integral equations by means of a scalable hierarchical matrix approach on clusters equipped with graphics hardware, i.e. graphics processing units (GPUs). To this end, we extend our…

Mathematical Software · Computer Science 2018-07-02 Helmut Harbrecht , Peter Zaspel

This paper presents a spectral element finite element scheme that efficiently solves elliptic problems on unstructured hexahedral meshes. The discrete equations are solved using a matrix-free preconditioned conjugate gradient algorithm. An…

Computational Engineering, Finance, and Science · Computer Science 2016-09-21 J. -F. Remacle , R. Gandham , T. Warburton

Many-particle continuous-time quantum walks (CTQWs) represent a resource for several tasks in quantum technology, including quantum search algorithms and universal quantum computation. In order to design and implement CTQWs in a realistic…

Quantum Physics · Physics 2017-10-02 Enrico Piccinini , Claudia Benedetti , Ilaria Siloi , Matteo G. A. Paris , Paolo Bordone

Process mapping asks to assign vertices of a task graph to processing elements of a supercomputer such that the computational workload is balanced while the communication cost is minimized. Motivated by the recent success of GPU-based graph…

Distributed, Parallel, and Cluster Computing · Computer Science 2026-03-16 Petr Samoldekin , Christian Schulz , Henning Woydt

As an important application of spatial databases in pathology imaging analysis, cross-comparing the spatial boundaries of a huge amount of segmented micro-anatomic objects demands extremely data- and compute-intensive operations, requiring…

Databases · Computer Science 2012-08-02 Kaibo Wang , Yin Huai , Rubao Lee , Fusheng Wang , Xiaodong Zhang , Joel H. Saltz