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The PC algorithm is the state-of-the-art algorithm for causal structure discovery on observational data. It can be computationally expensive in the worst case due to the conditional independence tests are performed in an…

Machine Learning · Computer Science 2021-09-13 Kai Zhang , Chao Tian , Kun Zhang , Todd Johnson , Xiaoqian Jiang

In this paper, first we give a sequential linear-time algorithm for the longest path problem in meshes. This algorithm can be considered as an improvement of [13]. Then based on this sequential algorithm, we present a constant-time parallel…

Data Structures and Algorithms · Computer Science 2012-01-24 Fatemeh Keshavarz-Kohjerdi , Alireza Bagheri

Chebyshev interpolation polynomials exhibit the exponential approximation property to analytic functions on a cube. Based on the Chebyshev interpolation polynomial approximation, we propose iterative polynomial approximation algorithms to…

Signal Processing · Electrical Eng. & Systems 2025-04-22 Cheng Cheng , Qiyu Sun , Cong Zheng

We describe an asynchronous parallel stochastic coordinate descent algorithm for minimizing smooth unconstrained or separably constrained functions. The method achieves a linear convergence rate on functions that satisfy an essential strong…

Optimization and Control · Mathematics 2014-11-12 Ji Liu , Stephen J. Wright , Christopher Ré , Victor Bittorf , Srikrishna Sridhar

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

Polynomial systems occur in many areas of science and engineering. Unlike general nonlinear systems, the algebraic structure enables to compute all solutions of a polynomial system. We describe our massive parallel predictor-corrector…

Mathematical Software · Computer Science 2015-05-05 Jan Verschelde , Xiangcheng Yu

In this article we present a parallel modular algorithm to compute all solutions with multiplicities of a given zero-dimensional polynomial system of equations over the rationals. In fact, we compute a triangular decomposition using…

Commutative Algebra · Mathematics 2013-06-12 Deeba Afzal , Faira Kanwal , Gerhard Pfister , Stefan Steidel

Hardware double precision is often insufficient to solve large scientific problems accurately. Computing in higher precision defined by software causes significant computational overhead. The application of parallel algorithms compensates…

Mathematical Software · Computer Science 2020-12-15 Jan Verschelde

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

Distributed Computation has been a recent trend in engineering research. Parallel Computation is widely used in different areas of Data Mining, Image Processing, Simulating Models, Aerodynamics and so forth. One of the major usage of…

Distributed, Parallel, and Cluster Computing · Computer Science 2017-03-28 C Rashmi

In this work, we present an extension of Gaussian process (GP) models with sophisticated parallelization and GPU acceleration. The parallelization scheme arises naturally from the modular computational structure w.r.t. datapoints in the…

Distributed, Parallel, and Cluster Computing · Computer Science 2014-10-21 Zhenwen Dai , Andreas Damianou , James Hensman , Neil Lawrence

We propose an algorithm for generating explicit solutions of multiparametric mixed-integer convex programs to within a given suboptimality tolerance. The algorithm is applicable to a very general class of optimization problems, but is most…

Optimization and Control · Mathematics 2019-06-12 Danylo Malyuta , Behcet Acikmese

The present paper proposes a new parallel algorithm for the modular division $u/v\bmod \beta^s$, where $u,\; v,\; \beta$ and $s$ are positive integers $(\beta\ge 2)$. The algorithm combines the classical add-and-shift multiplication scheme…

Distributed, Parallel, and Cluster Computing · Computer Science 2013-12-10 Sidi Mohamed Sedjelmaci , Christian Lavault

We propose investigating a summation analog of the paradigm for parallel integration. We make some first steps towards an indefinite summation method applicable to summands that rationally depend on the summation index and a P-recursive…

Combinatorics · Mathematics 2024-06-10 Shaoshi Chen , Ruyong Feng , Manuel Kauers , Xiuyun Li

We present a parallel solver for numerical constraint satisfaction problems (NCSPs) that can scale on a number of cores. Our proposed method runs worker solvers on the available cores and simultaneously the workers cooperate for the search…

Artificial Intelligence · Computer Science 2014-11-07 Daisuke Ishii , Kazuki Yoshizoe , Toyotaro Suzumura

Lenstra's integer factorization algorithm is asymptotically one of the fastest known algorithms, and is ideally suited for parallel computation. We suggest a way in which the algorithm can be speeded up by the addition of a second phase.…

Number Theory · Mathematics 2010-04-21 Richard P. Brent

Parallelization techniques have become ubiquitous for accelerating inference and training of deep neural networks. Despite this, several operations are still performed in a sequential manner. For instance, the forward and backward passes…

Machine Learning · Computer Science 2023-10-30 Federico Danieli , Miguel Sarabia , Xavier Suau , Pau Rodríguez , Luca Zappella

Multiplication of polynomials is among key operations in computer algebra which plays important roles in developing techniques for other commonly used polynomial operations such as division, evaluation/interpolation, and factorization. In…

Numerical Analysis · Mathematics 2022-06-02 S. Karami , M. Ahmadnasab , M. Hadizadeh , A. Amiraslani

An efficient quantum algorithm is proposed to solve in polynomial time the parity problem, one of the hardest problems both in conventional quantum computation and in classical computation, on NMR quantum computers. It is based on the…

Quantum Physics · Physics 2007-05-23 Xijia Miao

Integer factorization is one of the vital algorithms discussed as a part of analysis of any black-box cipher suites where the cipher algorithm is based on number theory. The origin of the problem is from Discrete Logarithmic Problem which…

Distributed, Parallel, and Cluster Computing · Computer Science 2013-05-21 Anjan K. Koundinya , Harish G. , Srinath N. K. , Raghavendra G. E. , Pramod Y. V. , Sandeep R. , Punith Kumar G