Parallel Factorization of Boolean Polynomials

2019 ◽  
pp. 80-94
Author(s):  
Vadiraj Kulkarni ◽  
Pavel Emelyanov ◽  
Denis Ponomaryov ◽  
Madhava Krishna ◽  
Soumyendu Raha ◽  
...  
Keyword(s):  
Parallel Factorization

On the parallel factorization of matrices over principal ideal rings

1999 ◽  
Vol 96 (2) ◽  
pp. 3022-3025
Author(s):  
V. M. Petrichkovich
Keyword(s):  
Principal Ideal ◽  
Parallel Factorization

GPU Accelerated Parallel Cholesky Factorization

2011 ◽  
Vol 148-149 ◽  
pp. 1370-1373 ◽  
Author(s):  
Liang Wang ◽  
Yi Sheng Zhang ◽  
Bin Zhu ◽  
Chi Xu ◽  
Xiao Wei Tian ◽  
...  
Keyword(s):  
Optimization Methods ◽  
Positive Definite ◽  
Cholesky Factorization ◽  
Positive Definite Matrices ◽  
Symmetric Positive Definite ◽  
Memory Scheduling ◽  
Parallel Factorization ◽  
Symmetric Positive Definite Matrices ◽  
Linear Equation Systems ◽  
Novel Algorithm

One of the fundamental problems in scientific computing is to find solutions for linear equation systems. For finite element problem, Cholesky factorization is often used to solve symmetric positive definite matrices. In this paper, Cholesky factorization is massively parallelized and three different optimization methods - highly parallel factorization, tile strategy and memory scheduling are used to accelerate Cholesky factorization effectively. A novel algorithm using OpenCL is implemented. Testing on GPU shows that performance of the algorithm increases with the dimension of matrix, reaching 785.41GFlops, about 50x times speedup. Cholesky factorization is remarkably improved with OpenCL on GPU.

scholarly journals Data-Driven and Low-Sparsity False Data Injection Attacks in Smart Grid

2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Jiwei Tian ◽  
Buhong Wang ◽  
Xia Li
Keyword(s):  
Optimization Techniques ◽  
Data Driven ◽  
Second Step ◽  
System Matrix ◽  
False Data Injection ◽  
Injection Attacks ◽  
Parallel Factorization ◽  
Three Stages ◽  
False Data Injection Attack ◽  
Attack Strategy

Recent researches on data-driven and low-sparsity data injection attacks have been presented, respectively. To combine the two main goals (data-driven and low-sparsity) of research, this paper presents a data-driven and low-sparsity false data injection attack strategy. The proposed attacking strategy (EID: Eliminate-Infer-Determine) is divided into three stages. In the first step, the intercepted data is preprocessed by sparse optimization techniques to eliminate the outliers. The recovered data is then exploited to learn about the system matrix based on the parallel factorization algorithm in the second step. In the third step, the approximated system matrix is applied for the design of sparse attack vector based on the convex optimization. The simulation results show that the EID attack strategy achieves a better performance than the improved ICA-based attack strategy in constructing perfect sparse attack vectors. What is more, data-driven implementation of the proposed strategy is also presented which ensures attack performance even without the prior information of the system.

A Fast Algorithm for Reordering Sparse Matrices for Parallel Factorization

1989 ◽  
Vol 10 (6) ◽  
pp. 1146-1173 ◽  
Author(s):  
John G. Lewis ◽  
Barry W. Peyton ◽  
Alex Pothen
Keyword(s):  
Fast Algorithm ◽  
Sparse Matrices ◽  
Parallel Factorization
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