An extended basis inexact shift–invert Lanczos for the efficient solution of large-scale generalized eigenproblems

2013 ◽  
Vol 184 (9) ◽  
pp. 2127-2135 ◽  
Author(s):  
M. Rewieński ◽  
A. Lamecki ◽  
M. Mrozowski
Keyword(s):  
Large Scale ◽  
Efficient Solution ◽  
Extended Basis

An Efficient Solution Algorithm for Large-Scale Stochastic Mixed-Integer Linear Programs1

2012 ◽  
Vol 45 (15) ◽  
pp. 892-897
Author(s):  
Arul Sundaramoorthy ◽  
Xiang Li ◽  
James M.B. Evans ◽  
Paul I. Barton
Keyword(s):  
Large Scale ◽  
Efficient Solution ◽  
Solution Algorithm ◽  
Mixed Integer

Reconfigurable architecture for the efficient solution of large-scale non-Hermitian eigenvalue problems

2006 ◽  
Author(s):  
Fernando E. Ortiz ◽  
Michael R. Bodnar ◽  
James P. Durbano ◽  
Eric J. Kelmelis
Keyword(s):  
Large Scale ◽  
Efficient Solution ◽  
Eigenvalue Problems ◽  
Reconfigurable Architecture

scholarly journals FABA: An Algorithm for Fast Aggregation against Byzantine Attacks in Distributed Neural Networks

2019 ◽  
Author(s):  
Qi Xia ◽  
Zeyi Tao ◽  
Zijiang Hao ◽  
Qun Li
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Deep Learning ◽  
Single Machine ◽  
Large Scale ◽  
Efficient Solution ◽  
Distributed Training ◽  
Hardware Failures ◽  
Deep Learning Neural Network ◽  
Byzantine Attacks

Many times, training a large scale deep learning neural network on a single machine becomes more and more difficult for a complex network model. Distributed training provides an efficient solution, but Byzantine attacks may occur on participating workers. They may be compromised or suffer from hardware failures. If they upload poisonous gradients, the training will become unstable or even converge to a saddle point. In this paper, we propose FABA, a Fast Aggregation algorithm against Byzantine Attacks, which removes the outliers in the uploaded gradients and obtains gradients that are close to the true gradients. We show the convergence of our algorithm. The experiments demonstrate that our algorithm can achieve similar performance to non-Byzantine case and higher efficiency as compared to previous algorithms.

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