scholarly journals Parallel Algorithm with Parameters Based on Alternating Direction for Solving Banded Linear Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Xinrong Ma ◽  
Sanyang Liu ◽  
Manyu Xiao ◽  
Gongnan Xie
Keyword(s):  
Parallel Algorithm ◽  
High Efficiency ◽  
Linear Equations ◽  
Positive Definite Matrix ◽  
Coefficient Matrix ◽  
Memory Space ◽  
Alternating Direction ◽  
Banded Linear Systems ◽  
Parallel Iterative ◽  
Better Than

An efficient parallel iterative method with parameters on distributed-memory multicomputer is investigated for solving the banded linear equations in this work. The parallel algorithm at each iterative step is executed using alternating direction by splitting the coefficient matrix and using parameters properly. Only it twice requires the communications of the algorithm between the adjacent processors, so this method has high parallel efficiency. Some convergence theorems for different coefficient matrices are given, such as a Hermite positive definite matrix or anM-matrix. Numerical experiments implemented on HP rx2600 cluster verify that our algorithm has the advantages over the multisplitting one of high efficiency and low memory space, which has a considerable advantage in CPU-times costs over the BSOR one. The efficiency for Example 1 is better than BSOR one significantly. As to Example 2, the acceleration rates and efficiency of our algorithm are better than the PEk inner iterative one.

Parallel Algorithm for Solving Block-Tridiagonal Linear Systems

2013 ◽  
Vol 427-429 ◽  
pp. 2420-2423
Author(s):  
Zhi Jian Duan
Keyword(s):  
Linear Systems ◽  
High Efficiency ◽  
Positive Definite Matrix ◽  
Coefficient Matrix ◽  
Iteration Step ◽  
Symmetric Positive Definite Matrix ◽  
Memory Space ◽  
Symmetric Positive Definite ◽  
Parallel Iterative ◽  
Parallel Acceleration

Efficient parallel iterative algorithm is investigated for solving block-tridiagonal linear systems on distributed-memory multi-computers. Based on Galerkin theory, the communication only need twice between the adjacent processors per iteration step. Furthermore, the condition for convergence is given when the coefficient matrix A is a symmetric positive definite matrix. Numerical experiments implemented on the cluster verify that our algorithm parallel acceleration rates and efficiency are higher than the multisplitting one, and has the advantages over the multisplitting method of high efficiency and low memory space.

scholarly journals Publicly verifiable and efficiency/security-adjustable outsourcing scheme for solving large-scale modular system of linear equations

2019 ◽  
Vol 8 (1) ◽  
Author(s):  
Panpan Meng ◽  
Chengliang Tian ◽  
Xiangguo Cheng
Keyword(s):  
Coding Theory ◽  
Large Scale ◽  
High Efficiency ◽  
Linear Equations ◽  
Coefficient Matrix ◽  
Secure Computation ◽  
Modular System ◽  
System Of Linear Equations ◽  
Public Verifiability ◽  
Cloud Server

AbstractSolving large-scale modular system of linear equations ($\mathcal {LMSLE}$ℒℳSℒE) is pervasive in modern computer and communication community, especially in the fields of coding theory and cryptography. However, it is computationally overloaded for lightweight devices arisen in quantity with the dawn of the things of internet (IoT) era. As an important form of cloud computing services, secure computation outsourcing has become a popular topic. In this paper, we design an efficient outsourcing scheme that enables the resource-constrained client to find a solution of the $\mathcal {LMSLE}$ℒℳSℒE with the assistance of a public cloud server. By utilizing affine transformation based on sparse unimodular matrices, our scheme has three merits compared with previous work: 1) Our scheme is efficiency/security-adjustable. Our encryption method is dynamic, and it can balance the security and efficiency to match different application scenarios by skillfully control the number of unimodular matrices. 2) Our scheme is versatile. It is suit for generic m-by-n coefficient matrix A, no matter it is square or not. 3) Our scheme satisfies public verifiability and achieves the optimal verification probability. It enables any verifier which is not necessarily the client to verify the correctness of the results returned from the cloud server with probability 1. Finally, theoretical analysis and comprehensive experimental results confirm our scheme’s security and high efficiency.

Solving Large-Scale Asymmetric Sparse Linear Equations Based on SuperLU Algorithm

2011 ◽  
Vol 230-232 ◽  
pp. 1355-1361
Author(s):  
Pei Wang ◽  
Xu Sheng Yang ◽  
Zhuo Yuan Wang ◽  
Lin Gong Li ◽  
Ji Chang He ◽  
...  
Keyword(s):  
Large Scale ◽  
Linear Equations ◽  
Computation Time ◽  
Coefficient Matrix ◽  
Memory Space ◽  
Storage Method

This article introduces the recent research of SuperLU algorithms and the optimal storage method for [1] the sparse linear equations of coefficient matrix. How to solve large-scale non-symmetric sparse linear equations by SuperLU algorithm is the key part of this article. The advantage of SuperLU algorithm compared to other algorithms is summarized at last. SuperLU algorithm not only saves memory space, but also reduces the computation time. Because of less storage needed by this algorithm, it could solve equation with larger scale, which is much more useful.

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.

scholarly journals A Globally Convergent Parallel SSLE Algorithm for Inequality Constrained Optimization

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Zhijun Luo ◽  
Lirong Wang
Keyword(s):  
Constrained Optimization ◽  
Optimization Problems ◽  
Linear Equations ◽  
Coefficient Matrix ◽  
Descent Direction ◽  
Constrained Optimization Problems ◽  
Inequality Constrained Optimization ◽  
Globally Convergent ◽  
Variable Distribution ◽  
Systems Of Linear Equations

A new parallel variable distribution algorithm based on interior point SSLE algorithm is proposed for solving inequality constrained optimization problems under the condition that the constraints are block-separable by the technology of sequential system of linear equation. Each iteration of this algorithm only needs to solve three systems of linear equations with the same coefficient matrix to obtain the descent direction. Furthermore, under certain conditions, the global convergence is achieved.

The use of faecal nitrogen as an index for estimating the consumption of herbage by grazing animals

1963 ◽  
Vol 61 (1) ◽  
pp. 33-43 ◽  
Author(s):  
G. W. Arnold ◽  
M. L. Dudzinski
Keyword(s):  
Organic Matter ◽  
Nitrogen Concentration ◽  
Linear Equations ◽  
Slope Position ◽  
Seasonal Differences ◽  
Faecal Nitrogen ◽  
Independent Variable ◽  
Regression Relations ◽  
The Relationship ◽  
Better Than

Data from thirty-five digestibility trials with sheep in metabolism cages were used to investigate statistically the relationships between organic matter intake (I), faecal organic matter output (F), and the nitrogen concentration in faecal organic matter (N).The data fell easily into groups due to botanical or seasonal differences in the feed. These groups of data were homogeneous and provided highly significant linear equations of the forms I = bF + cFN and I = a + cFN. When compared these groups of data sometimes showed differences in slope, position or both. A quadratic expressionI = bF + cFN + dFN2was found to accommodate a majority of the data but to be less precise than I = a + cFN.A further expression incorporating N as an independent variable was also examined,I = a + cFN2 + eN.This expression, although far from being universally adequate, proved to be generally better than existing formulae. When applied to the data of Greenhalgh et. al. (1960), it substantially reduced heterogeneity between data for spring and data for summer pastures.Causes of variation in the relationship between organic-matter intake and nitrogen in faeces, and some of the hazards of extrapolation from empirical regression relations, are discussed.

scholarly journals High-Efficiency Intracavity Continuous-Wave Green-Light Generation by Quasiphase Matching in a Bulk Periodically Poled MgO:LiNbO3 Crystal

2008 ◽  
Vol 2008 ◽  
pp. 1-4 ◽  
Author(s):  
Shaowei Chu ◽  
Ying Zhang ◽  
Bin Wang ◽  
Yong Bi
Keyword(s):  
High Efficiency ◽  
Continuous Wave ◽  
Green Light ◽  
Frequency Doubling ◽  
Green Laser ◽  
Periodically Poled ◽  
Output Stability ◽  
532 Nm ◽  
Better Than ◽  
Quasiphase Matching

908 mW of green light at 532 nm were generated by intracavity quasiphase matching in a bulk periodically poled MgO:LiNbO3 (PPMgLN) crystal. A maximum optical-to-optical conversion efficiency of 33.5% was obtained from a 0.5 mm thick, 10 mm long, and 5 mol% MgO:LiNbO3 crystal with an end-pump power of 2.7 W at 808 nm. The temperature bandwidth between the intracavity and single-pass frequency doubling was found to be different for the PPMgLN. Reliability and stability of the green laser were evaluated. It was found that for continuous operation of 100 hours, the output stability was better than 97.5% and no optical damage was observed.

Civil Aeroengine Fault Diagnosis Based on Fuzzy Least Square Support Vector Machine

2011 ◽  
Vol 130-134 ◽  
pp. 2047-2050 ◽  
Author(s):  
Hong Chun Qu ◽  
Xie Bin Ding
Keyword(s):  
Artificial Intelligence ◽  
Machine Learning ◽  
Support Vector Machine ◽  
Fault Diagnosis ◽  
Coefficient Matrix ◽  
Least Square ◽  
Support Vector ◽  
Influence Coefficient ◽  
Structural Risk ◽  
Better Than

SVM(Support Vector Machine) is a new artificial intelligence methodolgy, basing on structural risk mininization principle, which has better generalization than the traditional machine learning and SVM shows powerfulability in learning with limited samples. To solve the problem of lack of engine fault samples, FLS-SVM theory, an improved SVM, which is a method is applied. 10 common engine faults are trained and recognized in the paper.The simulated datas are generated from PW4000-94 engine influence coefficient matrix at cruise, and the results show that the diagnostic accuracy of FLS-SVM is better than LS-SVM.

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