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Several classic problems in graph processing and computational geometry are solved via incremental algorithms, which split computation into a series of small tasks acting on shared state, which gets updated progressively. While the…

Data Structures and Algorithms · Computer Science 2020-03-24 Dan Alistarh , Nikita Koval , Giorgi Nadiradze

Decoupling multivariate polynomials is useful for obtaining an insight into the workings of a nonlinear mapping, performing parameter reduction, or approximating nonlinear functions. Several different tensor-based approaches have been…

Numerical Analysis · Mathematics 2019-01-31 Konstantin Usevich , Philippe Dreesen , Mariya Ishteva

We are concerned with the problem of decomposing the parameter space of a parametric system of polynomial equations, and possibly some polynomial inequality constraints, with respect to the number of real solutions that the system attains.…

Symbolic Computation · Computer Science 2022-02-11 AmirHosein Sadeghimanesh , Matthew England

The efficient solution of moderately large-scale linear systems arising from the KKT conditions in optimal control problems (OCPs) is a critical challenge in robotics. With the stagnation of Moore's law, there is growing interest in…

Optimization and Control · Mathematics 2025-05-21 Shaohui Yang , Toshiyuki Ohtsuka , Brian Plancher , Colin N. Jones

In this paper, we propose an efficient parallelization strategy for boundary element method (BEM) solvers that perform the electromagnetic analysis of structures with lossy conductors. The proposed solver is accelerated with the adaptive…

Distributed, Parallel, and Cluster Computing · Computer Science 2022-11-30 Damian Marek , Shashwat Sharma , Piero Triverio

We present and compare distributed parallelization strategies for the particle-in-Fourier (PIF) schemes used in kinetic plasma simulations. The different strategies are i) domain decomposition, where both the particles and Fourier modes are…

Computational Engineering, Finance, and Science · Computer Science 2026-05-12 Sriramkrishnan Muralikrishnan , Paul Fischill , Andreas Adelmann , Robert Speck

In this paper we review the parallel solution of sparse linear systems, usually deriving by the discretization of ODE-IVPs or ODE-BVPs. The approach is based on the concept of parallel factorization of a (block) tridiagonal matrix. This…

Numerical Analysis · Mathematics 2010-01-13 Pierluigi Amodio , Luigi Brugnano

Geometric modeling by constraints leads to large systems of algebraic equations. This paper studies bipartite graphs underlaid by systems of equations. It shows how these graphs make possible to polynomially decompose these systems into…

Discrete Mathematics · Computer Science 2014-05-26 Samy Ait-Aoudia , Roland Jegou , Dominique Michelucci

Graph clustering has many important applications in computing, but due to growing sizes of graphs, even traditionally fast clustering methods such as spectral partitioning can be computationally expensive for real-world graphs of interest.…

Distributed, Parallel, and Cluster Computing · Computer Science 2019-06-11 Julian Shun , Farbod Roosta-Khorasani , Kimon Fountoulakis , Michael W. Mahoney

Nonclassical symmetries and reductions of polynomial equations and systems of polynomial equations are considered. It is shown that specific polynomial equations having "hidden" symmetries can be reduced to classical symmetric systems of…

Numerical Analysis · Mathematics 2026-01-22 Inna K. Shingareva , Andrei D. Polyanin

This work presents a parallel variant of the algorithm introduced in [Acceleration of block coordinate descent methods with identification strategies Comput. Optim. Appl. 72(3):609--640, 2019] to minimize the sum of a partially separable…

Optimization and Control · Mathematics 2025-08-06 Ronaldo Lopes , Sandra A. Santos , Paulo J. S. Silva

Many parallel algorithms which solve basic problems in computer science use auxiliary space linear in the input to facilitate conflict-free computation. There has been significant work on improving these parallel algorithms to be in-place,…

Data Structures and Algorithms · Computer Science 2025-03-11 Chase Hutton , Adam Melrod

Numerically solving ordinary differential equations (ODEs) is a naturally serial process and as a result the vast majority of ODE solver software are serial. In this manuscript we developed a set of parallelized ODE solvers using…

Numerical Analysis · Mathematics 2022-09-13 Utkarsh , Chris Elrod , Yingbo Ma , Christopher Rackauckas

We propose a decomposition framework for the parallel optimization of the sum of a differentiable function and a (block) separable nonsmooth, convex one. The latter term is typically used to enforce structure in the solution as, for…

Distributed, Parallel, and Cluster Computing · Computer Science 2013-11-12 Francisco Facchinei , Simone Sagratella , Gesualdo Scutari

In this paper we describe a numerical method designed for modelling different kinds of astrophysical flows in three dimensions. Our method is a standard explicit finite difference method employing the local shearing-box technique. To model…

Astrophysics · Physics 2009-11-06 S. E. Caunt , M. J. Korpi

We study the question of whether parallelization in the exploration of the feasible set can be used to speed up convex optimization, in the local oracle model of computation. We show that the answer is negative for both deterministic and…

Optimization and Control · Mathematics 2019-06-21 Jelena Diakonikolas , Cristóbal Guzmán

In this paper we propose a new inexact dual decomposition algorithm for solving separable convex optimization problems. This algorithm is a combination of three techniques: dual Lagrangian decomposition, smoothing and excessive gap. The…

Optimization and Control · Mathematics 2013-02-11 Quoc Tran Dinh , Ion Necoara , Moritz Diehl

The generalized method to have a parallel solution to a computational problem, is to find a way to use Divide & Conquer paradigm in order to have processors acting on its own data and therefore all can be scheduled in parallel. MapReduce is…

Distributed, Parallel, and Cluster Computing · Computer Science 2015-10-13 Julián Aráoz , Cristina Zoltan

Harnessing parallelism in seemingly sequential models is a central challenge for modern machine learning. Several approaches have been proposed for evaluating sequential processes in parallel using iterative fixed-point methods, like…

Recent advances in random-walk particle-tracking have enabled direct simulation of mixing and reactions on particles by allowing the particles to interact with each other using a multi-point mass transfer scheme. The mass transfer scheme…

Computational Physics · Physics 2019-04-22 Nicholas B. Engdahl , Michael J. Schmidt , David A. Benson