Alternating direction splitting for block Angular parallel optimization

1996 ◽  
Vol 90 (1) ◽  
pp. 1-29 ◽  
Author(s):  
S. Kontogiorgis ◽  
R. De Leone ◽  
R. R. Meyer
Keyword(s):  
Parallel Optimization ◽  
Alternating Direction ◽  
Direction Splitting

scholarly journals IMPROVED ACCURACY FOR ALTERNATING-DIRECTION METHODS FOR PARABOLIC EQUATIONS BASED ON REGULAR AND MIXED FINITE ELEMENTS

2007 ◽  
Vol 17 (08) ◽  
pp. 1279-1305 ◽  
Author(s):  
TODD ARBOGAST ◽  
CHIEH-SEN HUANG ◽  
SONG-MING YANG
Keyword(s):  
Finite Element ◽  
Mixed Finite Element ◽  
Mixed Finite Elements ◽  
Time Step ◽  
Galerkin Finite Element ◽  
Alternating Direction ◽  
Direction Splitting ◽  
Proposed Modification ◽  
Alternating Directions Method ◽  
Improved Accuracy

An efficient modification by Douglas and Kim of the usual alternating directions method reduces the splitting error from [Formula: see text] to [Formula: see text] in time step k. We prove convergence of this modified alternating directions procedure, for the usual non-mixed Galerkin finite element and finite difference cases, under the restriction that k/h2 is sufficiently small, where h is the grid spacing. This improves the results of Douglas and Gunn, who require k/h4 to be sufficiently small, and Douglas and Kim, who require that the locally one-dimensional operators commute. We propose a similar and efficient modification of alternating directions for mixed finite element methods that reduces the splitting error to [Formula: see text], and we prove convergence in the noncommuting case, provided that k/h2 is sufficiently small. Numerical computations illustrating the mixed finite element results are also presented. They show that our proposed modification can lead to a significant reduction in the alternating direction splitting error.

Performance analysis of various massive MIMO detection algorithms in 5G Wireless technologies

2019 ◽  
Vol 10 ◽  
Author(s):  
Shihab Jimaa ◽  
Jawahir Al-Ali
Keyword(s):  
Massive Mimo ◽  
Spectrum Efficiency ◽  
System Capacity ◽  
Network Coverage ◽  
Mimo Detection ◽  
Infinity Norm ◽  
Detection Algorithms ◽  
Alternating Direction ◽  
5G Systems ◽  
Efficient Power

Background: The 5G will lead to a great transformation in the mobile telecommunications sector. Objective: The huge challenges being faced by wireless communications such as the increased number of users have given a chance for 5G systems to be developed and considered as an alternative solution. The 5G technology will provide a higher data rate, reduced latency, more efficient power than the previous generations, higher system capacity, and more connected devices. Method: It will offer new different technologies and enhanced versions of the existing ones, as well as new features. 5G systems are going to use massive MIMO (mMIMO), which is a promising technology in the development of these systems. Furthermore, mMIMO will increase the wireless spectrum efficiency and improve the network coverage. Result: In this paper we present a brief survey on 5G and its technologies, discuss the mMIMO technology with its features and advantages, review the mMIMO capacity and energy efficiency and also presents the recent beamforming techniques. Conclusion: Finally, simulation of adopting different mMIMO detection algorithms are presented, which shows the alternating direction method of multipliers (ADMM)-based infinity-norm (ADMIN) detector has the best performance.

scholarly journals ECG Signal Denoising and Reconstruction Based on Basis Pursuit

2021 ◽  
Vol 11 (4) ◽  
pp. 1591
Author(s):  
Ruixia Liu ◽  
Minglei Shu ◽  
Changfang Chen
Keyword(s):  
Signal To Noise Ratio ◽  
Heart Diseases ◽  
Gaussian White Noise ◽  
Basis Pursuit ◽  
Signal Denoising ◽  
Ecg Signal ◽  
Penalty Term ◽  
Ecg Signals ◽  
Alternating Direction ◽  
Low Pass

The electrocardiogram (ECG) is widely used for the diagnosis of heart diseases. However, ECG signals are easily contaminated by different noises. This paper presents efficient denoising and compressed sensing (CS) schemes for ECG signals based on basis pursuit (BP). In the process of signal denoising and reconstruction, the low-pass filtering method and alternating direction method of multipliers (ADMM) optimization algorithm are used. This method introduces dual variables, adds a secondary penalty term, and reduces constraint conditions through alternate optimization to optimize the original variable and the dual variable at the same time. This algorithm is able to remove both baseline wander and Gaussian white noise. The effectiveness of the algorithm is validated through the records of the MIT-BIH arrhythmia database. The simulations show that the proposed ADMM-based method performs better in ECG denoising. Furthermore, this algorithm keeps the details of the ECG signal in reconstruction and achieves higher signal-to-noise ratio (SNR) and smaller mean square error (MSE).

scholarly journals Correction to: Parallel optimization of the ray-tracing algorithm based on the HPM model

2021 ◽  
Author(s):  
Wang Jun-Feng ◽  
Ding Gang-Yi ◽  
Wang Yi-Ou ◽  
Li Yu-Gang ◽  
Zhang Fu-Quan
Keyword(s):  
Ray Tracing ◽  
Parallel Optimization ◽  
Tracing Algorithm

scholarly journals Image smoothing based on global sparsity decomposition and a variable parameter

2021 ◽  
Author(s):  
Xiang Ma ◽  
Xuemei Li ◽  
Yuanfeng Zhou ◽  
Caiming Zhang
Keyword(s):  
Removal Rate ◽  
Variable Parameter ◽  
Smoothing Parameter ◽  
Smoothing Effect ◽  
Image Smoothing ◽  
Sparse Decomposition ◽  
Alternating Direction ◽  
Texture Removal ◽  
Ideal Algorithm ◽  
Better Than

AbstractSmoothing images, especially with rich texture, is an important problem in computer vision. Obtaining an ideal result is difficult due to complexity, irregularity, and anisotropicity of the texture. Besides, some properties are shared by the texture and the structure in an image. It is a hard compromise to retain structure and simultaneously remove texture. To create an ideal algorithm for image smoothing, we face three problems. For images with rich textures, the smoothing effect should be enhanced. We should overcome inconsistency of smoothing results in different parts of the image. It is necessary to create a method to evaluate the smoothing effect. We apply texture pre-removal based on global sparse decomposition with a variable smoothing parameter to solve the first two problems. A parametric surface constructed by an improved Bessel method is used to determine the smoothing parameter. Three evaluation measures: edge integrity rate, texture removal rate, and gradient value distribution are proposed to cope with the third problem. We use the alternating direction method of multipliers to complete the whole algorithm and obtain the results. Experiments show that our algorithm is better than existing algorithms both visually and quantitatively. We also demonstrate our method’s ability in other applications such as clip-art compression artifact removal and content-aware image manipulation.

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