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Thermodynamic computing has emerged as a promising paradigm for accelerating computation by harnessing the thermalization properties of physical systems. This work introduces a novel approach to solving quadratic programming problems using…

We present a new continuation algorithm to find all nondegenerate real solutions to a system of polynomial equations. Unlike homotopy methods, it is not based on a deformation of the system; instead, it traces real curves connecting the…

Algebraic Geometry · Mathematics 2009-09-01 Dan Bates , Frank Sottile

The main objective of this work consists in analyzing sub-structuring method for the parallel solution of sparse linear systems with matrices arising from the discretization of partial differential equations such as finite element, finite…

Numerical Analysis · Mathematics 2021-08-31 Abal-Kassim Cheik Ahamed , Frédéric Magoulès

Graphics processing units (GPU) had evolved from a specialized hardware capable to render high quality graphics in games to a commodity hardware for effective processing blocks of data in a parallel schema. This evolution is particularly…

Distributed, Parallel, and Cluster Computing · Computer Science 2012-03-26 Luis Cabellos

We propose a CPU-GPU heterogeneous computing method for solving time-evolution partial differential equation problems many times with guaranteed accuracy, in short time-to-solution and low energy-to-solution. On a single-GH200 node, the…

Computational Engineering, Finance, and Science · Computer Science 2024-10-01 Tsuyoshi Ichimura , Kohei Fujita , Muneo Hori , Lalith Maddegedara , Jack Wells , Alan Gray , Ian Karlin , John Linford

Much combinatorial optimisation problems constitute a non-polynomial (NP) hard optimisation problem, i.e., they can not be solved in polynomial time. One such problem is finding the shortest route between two nodes on a graph.…

Machine Learning · Statistics 2017-09-08 Alessandro Bay , Biswa Sengupta

On modern architectures, the performance of 32-bit operations is often at least twice as fast as the performance of 64-bit operations. By using a combination of 32-bit and 64-bit floating point arithmetic, the performance of many dense and…

Mathematical Software · Computer Science 2015-05-13 Marc Baboulin , Alfredo Buttari , Jack Dongarra , Jakub Kurzak , Julie Langou , Julien Langou , Piotr Luszczek , Stanimire Tomov

We design, implement, and evaluate GPU-based algorithms for the maximum cardinality matching problem in bipartite graphs. Such algorithms have a variety of applications in computer science, scientific computing, bioinformatics, and other…

Distributed, Parallel, and Cluster Computing · Computer Science 2013-03-07 Mehmet Deveci , Kamer Kaya , Bora Ucar , Umit V. Catalyurek

We present a homotopic approach to solving challenging, optimization-based motion planning problems. The approach uses Homotopy Optimization, which, unlike standard continuation methods for solving homotopy problems, solves a sequence of…

Robotics · Computer Science 2024-08-23 Shayan Pardis , Matthew Chignoli , Sangbae Kim

We present a convex hull algorithm that is accelerated on commodity graphics hardware. We analyze and identify the hurdles of writing a recursive divide and conquer algorithm on the GPU and divise a framework for representing this class of…

Computational Geometry · Computer Science 2015-03-20 Stanley Tzeng , John D. Owens

High fidelity scientific simulations modeling physical phenomena typically require solving large linear systems of equations which result from discretization of a partial differential equation (PDE) by some numerical method. This step often…

Mathematical Software · Computer Science 2020-07-01 Mohammad Shafaet Islam , Qiqi Wang

We equip dynamic geometry software (DGS) with a user-friendly method that enables massively parallel calculations on the graphics processing unit (GPU). This interplay of DGS and GPU opens up various applications in education and…

Mathematical Software · Computer Science 2018-08-15 Aaron Montag , Jürgen Richter-Gebert

We study the cost of multiplication modulo triangular families of polynomials. Following previous work by Li, Moreno Maza and Schost, we propose an algorithm that relies on homotopy and fast evaluation-interpolation techniques. We obtain a…

Symbolic Computation · Computer Science 2009-01-26 Alin Bostan , Muhammad Chowdhury , Joris van der Hoeven , Eric Schost

The Graph Isomorphism (GI) problem is a theoretically interesting problem because it has not been proven to be in P nor to be NP-complete. Babai made a breakthrough in 2015 when announcing a quasipolynomial time algorithm for GI problem.…

Data Structures and Algorithms · Computer Science 2020-02-13 Duc Hung Pham , Krishna V. Palem , M. V. Panduranga Rao

In this paper an algorithm is given to determine all possible structurally different linearly conjugate realizations of a given kinetic polynomial system. The solution is based on the iterative search for constrained dense realizations…

Dynamical Systems · Mathematics 2016-03-08 Bernadett Acs , Gabor Szederkenyi , Zsolt Tuza , Zoltan Andras Tuza

We propose a new algorithm for multiplying dense polynomials with integer coefficients in a parallel fashion, targeting multi-core processor architectures. Complexity estimates and experimental comparisons demonstrate the advantages of this…

Symbolic Computation · Computer Science 2016-12-20 Changbo Chen , Svyatoslav Covanov , Farnam Mansouri , Marc Moreno Maza , Ning Xie , Yuzhen Xie

We describe a method for parallelizing the lexicographic enumeration algorithm for the factorization set of an element in a numerical semigroup via bounds. This enables the use of GPU and distributed computing methods. We provide a CUDA…

Commutative Algebra · Mathematics 2024-05-14 Thomas Barron

This paper presents a high-accuracy higher-order multiscale method for solving multi-continuum problems in in highly heterogeneous media. First, microscopic unit cell functions are defined, leading to the derivation of macroscopic…

Numerical Analysis · Mathematics 2026-04-08 Hao Dong , Jiayuan Peng , Jian Huang

The notion of graph covers (also referred to as locally bijective homomorphisms) plays an important role in topological graph theory and has found its computer science applications in models of local computation. For a fixed target graph…

Discrete Mathematics · Computer Science 2025-02-28 Jan Bok , Jiří Fiala , Nikola Jedličková , Jan Kratochvíl , Micheala Seifrtová

In recent years graphical processing units (GPUs) have become a powerful tool in scientific computing. Their potential to speed up highly parallel applications brings the power of high performance computing to a wider range of users.…

Distributed, Parallel, and Cluster Computing · Computer Science 2017-04-26 Uldis Locans , Andreas Adelmann , Andreas Suter , Jannis Fischer , Werner Lustermann , Gunther Dissertori , Qiulin Wang