Parallel numerical asynchronous iterative algorithms: Large scale experimentations

2009 ◽  
Author(s):  
Jean-Claude Charr ◽  
Raphael Couturier ◽  
David Laiymani
Keyword(s):  
Large Scale ◽  
Iterative Algorithms

scholarly journals Alternating Asymmetric Iterative Algorithm Based on Domain Decomposition for 3D Poisson Problem

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 281
Author(s):  
Qiuyan Xu ◽  
Zhiyong Liu
Keyword(s):  
Domain Decomposition ◽  
Iterative Algorithm ◽  
Poisson Equation ◽  
Large Scale ◽  
Linear Equations ◽  
Iterative Algorithms ◽  
Computation Time ◽  
Explicit Method ◽  
Computational Process ◽  
Poisson Problem

Poisson equation is a widely used partial differential equation. It is very important to study its numerical solution. Based on the strategy of domain decomposition, the alternating asymmetric iterative algorithm for 3D Poisson equation is provided. The solution domain is divided into several sub-domains, and eight asymmetric iterative schemes with the relaxation factor for 3D Poisson equation are constructed. When the numbers of iteration are odd or even, the computational process of the presented iterative algorithm are proposed respectively. In the calculation of the inner interfaces, the group explicit method is used, which makes the algorithm to be performed fast and in parallel, and avoids the difficulty of solving large-scale linear equations. Furthermore, the convergence of the algorithm is analyzed theoretically. Finally, by comparing with the numerical experimental results of Jacobi and Gauss Seidel iterative algorithms, it is shown that the alternating asymmetric iterative algorithm based on domain decomposition has shorter computation time, fewer iteration numbers and good parallelism.

Iterative Algorithms for Large Scale Wave Front Reconstruction

2001 ◽  
Author(s):  
Luc Gilles ◽  
Curtis R. Vogel ◽  
Brent L. Ellerbroek
Keyword(s):  
Wave Front ◽  
Large Scale ◽  
Iterative Algorithms

Iterative Algorithms to Generate Large Scale Mosaic Images

2015 ◽  
pp. 203-208 ◽  
Author(s):  
Lorenzo Toso ◽  
Stephan Allgeier ◽  
Franz Eberle ◽  
Susanne Maier ◽  
Klaus-Martin Reichert ◽  
...  
Keyword(s):  
Large Scale ◽  
Iterative Algorithms ◽  
Mosaic Images

A Study of Sparse Matrix Methods on New Hardware

2015 ◽  
Vol 3 (3) ◽  
pp. 1-19
Author(s):  
Athanasios Fevgas ◽  
Konstantis Daloukas ◽  
Panagiota Tsompanopoulou ◽  
Panayiotis Bozanis
Keyword(s):  
Power Systems ◽  
Linear Systems ◽  
Large Scale ◽  
Comprehensive Evaluation ◽  
Sparse Matrix ◽  
Electrical Power ◽  
Iterative Algorithms ◽  
Direct Methods ◽  
Computer Hardware ◽  
Computing Platforms

Modeling of numerous scientific and engineering problems, such as multi-physic problems and analysis of electrical power systems, amounts to the solution of large scale linear systems. The main characteristics of such systems are the large sparsity ratio and the large number of unknowns that can reach thousands or even millions of equations. As a result, efficient solution of sparse large-scale linear systems is of great importance in order to enable analysis of such problems. Direct and iterative algorithms are the prevalent methods for solution of linear systems. Advances in computer hardware provide new challenges and capabilities for sparse solvers. The authors present a comprehensive evaluation of some, state of the art, sparse methods (direct and iterative) using modern computing platforms, aiming to determine the performance boundaries of each solver on different hardware infrastructures. By identifying the potential performance bottlenecks of out-of-core direct methods, the authors present a series of optimizations that increase their efficiency on flash-based systems.

PARALLEL DISTRIBUTED SOLVERS FOR LARGE STABLE GENERALIZED LYAPUNOV EQUATIONS

1999 ◽  
Vol 09 (01) ◽  
pp. 147-158 ◽  
Author(s):  
PETER BENNER ◽  
JOSÉ M. CLAVER ◽  
ENRIQUE S. QUINTANA-ORTI
Keyword(s):  
Large Scale ◽  
Iterative Algorithms ◽  
Direct Methods ◽  
Matrix Equations ◽  
Distributed Architectures ◽  
Matrix Sign Function ◽  
Sign Function ◽  
The Matrix ◽  
Qz Algorithm ◽  
Lyapunov Matrix

In this paper we study the solution of stable generalized Lyapunov matrix equations with large-scale, dense coefficient matrices. Our iterative algorithms, based on the matrix sign function, only require scalable matrix algebra kernels which are highly efficient on parallel distributed architectures. This approach avoids therefore the difficult parallelization of direct methods based on the QZ algorithm. The experimental analtsis reports a remarkable performance of our solvers on an IBM SP2 platform.

scholarly journals An Efficient Three-Term Iterative Method for Estimating Linear Approximation Models in Regression Analysis

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 977
Author(s):  
Siti Farhana Husin ◽  
Mustafa Mamat ◽  
Mohd Asrul Hery Ibrahim ◽  
Mohd Rivaie
Keyword(s):  
Iterative Method ◽  
Regression Model ◽  
Large Scale ◽  
Optimization Problems ◽  
Numerical Algorithms ◽  
Iterative Algorithms ◽  
Test Problems ◽  
Exact Line Search ◽  
Unconstrained Optimization Problems ◽  
Large Scale Unconstrained Optimization

This study employs exact line search iterative algorithms for solving large scale unconstrained optimization problems in which the direction is a three-term modification of iterative method with two different scaled parameters. The objective of this research is to identify the effectiveness of the new directions both theoretically and numerically. Sufficient descent property and global convergence analysis of the suggested methods are established. For numerical experiment purposes, the methods are compared with the previous well-known three-term iterative method and each method is evaluated over the same set of test problems with different initial points. Numerical results show that the performances of the proposed three-term methods are more efficient and superior to the existing method. These methods could also produce an approximate linear regression equation to solve the regression model. The findings of this study can help better understanding of the applicability of numerical algorithms that can be used in estimating the regression model.

scholarly journals Convergence Results on Iteration Algorithms to Linear Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Zhuande Wang ◽  
Chuansheng Yang ◽  
Yubo Yuan
Keyword(s):  
Linear Systems ◽  
Spectral Radius ◽  
Positive Constant ◽  
Numerical Experiments ◽  
Large Scale ◽  
Iterative Algorithms ◽  
Convergence Results ◽  
Jacobi Iteration ◽  
The One

In order to solve the large scale linear systems, backward and Jacobi iteration algorithms are employed. The convergence is the most important issue. In this paper, a unified backward iterative matrix is proposed. It shows that some well-known iterative algorithms can be deduced with it. The most important result is that the convergence results have been proved. Firstly, the spectral radius of the Jacobi iterative matrix is positive and the one of backward iterative matrix is strongly positive (lager than a positive constant). Secondly, the mentioned two iterations have the same convergence results (convergence or divergence simultaneously). Finally, some numerical experiments show that the proposed algorithms are correct and have the merit of backward methods.

scholarly journals Solving Imperfect-Information Games via Discounted Regret Minimization

2019 ◽  
Vol 33 ◽  
pp. 1829-1836 ◽  
Author(s):  
Noam Brown ◽  
Tuomas Sandholm
Keyword(s):  
Imperfect Information ◽  
Large Scale ◽  
State Of The Art ◽  
Iterative Algorithms ◽  
Game Tree ◽  
Regret Minimization ◽  
Imperfect Information Games ◽  
Improved Performance ◽  
Pruning Techniques ◽  
Prior State

Counterfactual regret minimization (CFR) is a family of iterative algorithms that are the most popular and, in practice, fastest approach to approximately solving large imperfectinformation games. In this paper we introduce novel CFR variants that 1) discount regrets from earlier iterations in various ways (in some cases differently for positive and negative regrets), 2) reweight iterations in various ways to obtain the output strategies, 3) use a non-standard regret minimizer and/or 4) leverage “optimistic regret matching”. They lead to dramatically improved performance in many settings. For one, we introduce a variant that outperforms CFR+, the prior state-of-the-art algorithm, in every game tested, including large-scale realistic settings. CFR+ is a formidable benchmark: no other algorithm has been able to outperform it. Finally, we show that, unlike CFR+, many of the important new variants are compatible with modern imperfect-informationgame pruning techniques and one is also compatible with sampling in the game tree.

A NEW PLATFORM FOR THE IMPLEMENTATION OF REGULAR ITERATIVE ALGORITHMS INTO FPGAs

2011 ◽  
Vol 20 (06) ◽  
pp. 975-999
Author(s):  
STAVROS P. DOKOUZYANNIS ◽  
ARGIRIS P. MOKIOS
Keyword(s):  
Large Scale ◽  
New Technology ◽  
Iterative Algorithms ◽  
Computer Arithmetic ◽  
Design Tool ◽  
Systolic Arrays ◽  
Field Programmable ◽  
Large Scale Integration ◽  
Scale Integration ◽  
Vlsi Chips

The implementation of regular iterative algorithms (RIAs) in important scientific fields such as image processing, computer arithmetic, cryptography and their implementation in processor arrays architectures, has been extensively studied over the last three decades. Numerous design methodologies and tools have been proposed, mostly targeting custom very large scale integration (VLSI) chips. The advent of field-programmable gate arrays (FPGAs) has attracted many researchers to incorporate previously acquired knowledge and experience in designing VLSI chips, to this new technology. This paper addresses the issue of the implementation of regular algorithms into FPGAs and presents a novel design tool for the implementation of RIAs, formulated as dependence graphs (DGs), on systolic arrays. Furthermore, a platform scheme for the systolic arrays hardware realization is proposed.

scholarly journals Sketched Iterative Algorithms for Structured Generalized Linear Models

2019 ◽  
Author(s):  
Qilong Gu ◽  
Arindam Banerjee
Keyword(s):  
Large Scale ◽  
Linear Models ◽  
Iterative Algorithms ◽  
Statistical Error ◽  
Trade Offs ◽  
Original Dataset ◽  
Geometric Convergence ◽  
Estimation Problems ◽  
Reduced Gradient ◽  
Projected Gradient Descent

Recent years have seen advances in optimizing large scale statistical estimation problems. In statistical learning settings iterative optimization algorithms have been shown to enjoy geometric convergence. While powerful, such results only hold for the original dataset, and may face computational challenges when the sample size is large. In this paper, we study sketched iterative algorithms, in particular sketched-PGD (projected gradient descent) and sketched-SVRG (stochastic variance reduced gradient) for structured generalized linear model, and illustrate that these methods continue to have geometric convergence to the statistical error under suitable assumptions. Moreover, the sketching dimension is allowed to be even smaller than the ambient dimension, thus can lead to significant speed-ups. The sketched iterative algorithms introduced provide an additional dimension to study the trade-offs between statistical accuracy and time.

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