Comparison results for splitting iterations for solving multi-linear systems

2018 ◽  
Vol 134 ◽  
pp. 105-121 ◽  
Author(s):  
Wen Li ◽  
Dongdong Liu ◽  
Seak-Weng Vong
Keyword(s):  
Linear Systems ◽  
Comparison Results

scholarly journals Block Preconditioned SSOR Methods for -Matrices Linear Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Zhao-Nian Pu ◽  
Xue-Zhong Wang
Keyword(s):  
Linear System ◽  
Linear Systems ◽  
Iterative Methods ◽  
Spectral Radius ◽  
Numerical Examples ◽  
Comparison Results ◽  
Block Preconditioner

We present a block preconditioner and consider block preconditioned SSOR iterative methods for solving linear system . When is an -matrix, the convergence and some comparison results of the spectral radius for our methods are given. Numerical examples are also given to illustrate that our methods are valid.

Comparison Results between Jacobi and USSOR Iterative Methods

2014 ◽  
Vol 989-994 ◽  
pp. 1790-1793
Author(s):  
Ting Zhou ◽  
Shi Guang Zhang
Keyword(s):  
Linear Systems ◽  
Iterative Methods ◽  
Spectral Radius ◽  
Numerical Example ◽  
Iteration Matrix ◽  
Comparison Results ◽  
Jacobi Iteration

In this paper, some comparison results between Jacobi and USSOR iteration for solving nonsingular linear systems are presented. It is showed that spectral radius of Jacobi iteration matrix B is less than that of USSOR iterative matrix under some conditions. A numerical example is also given to illustrate our results.

scholarly journals A modified AOR-type iterative method for L-matrix linear systems

2007 ◽  
Vol 49 (2) ◽  
pp. 281-292 ◽  
Author(s):  
Shiliang Wu ◽  
Tingzhu Huang
Keyword(s):  
Iterative Method ◽  
Linear Systems ◽  
Iterative Methods ◽  
Convergence Rates ◽  
Comparison Theorems ◽  
Iterative Schemes ◽  
Seidel Method ◽  
Comparison Results ◽  
Preconditioned Iterative ◽  
Preconditioned Iterative Methods

AbstractBoth Evans et al. and Li et al. have presented preconditioned methods for linear systems to improve the convergence rates of AOR-type iterative schemes. In this paper, we present a new preconditioner. Some comparison theorems on preconditioned iterative methods for solving L-matrix linear systems are presented. Comparison results and a numerical example show that convergence of the preconditioned Gauss-Seidel method is faster than that of the preconditioned AOR iterative method.

scholarly journals Convergence theory of iterative methods based on proper splittings and proper multisplittings for rectangular linear systems

Filomat ◽  
2020 ◽  
Vol 34 (6) ◽  
pp. 1835-1851
Author(s):  
Vaibhav Shekhar ◽  
Chinmay Giri ◽  
Debasisha Mishra
Keyword(s):  
Linear Systems ◽  
Iterative Scheme ◽  
Iterative Solution ◽  
Differential Algebraic Equations ◽  
Convergence Theory ◽  
Algebraic Equations ◽  
Linear System Of Equations ◽  
Convergence Results ◽  
Comparison Results ◽  
Singular Linear System

Multisplitting methods are useful to solve differential-algebraic equations. In this connection, we discuss the theory of matrix splittings and multisplittings, which can be used for finding the iterative solution of a large class of rectangular (singular) linear system of equations of the form Ax = b. In this direction, many convergence results are proposed for different subclasses of proper splittings in the literature. But, in some practical cases, the convergence speed of the iterative scheme is very slow. To overcome this issue, several comparison results are obtained for different subclasses of proper splittings. This paper also presents a few such results. However, this idea fails to accelerate the speed of the iterative scheme in finding the iterative solution. In this regard, Climent and Perea [J. Comput. Appl. Math. 158 (2003), 43-48: MR2013603] introduced the notion of proper multisplittings to solve the system Ax = b on parallel and vector machines, and established convergence theory for a subclass of proper multisplittings. With the aim to extend the convergence theory of proper multisplittings, this paper further adds a few results. Some of the results obtained in this paper are even new for the iterative theory of nonsingular linear systems.

scholarly journals Convergence Analysis of Preconditioned AOR Iterative Method for Linear Systems

2010 ◽  
Vol 2010 ◽  
pp. 1-14 ◽  
Author(s):  
Qingbing Liu ◽  
Guoliang Chen
Keyword(s):  
Iterative Method ◽  
Rate Of Convergence ◽  
Linear Systems ◽  
Optimization Theory ◽  
Convergence Result ◽  
Comparison Theorems ◽  
Car Industry ◽  
Fluid Analysis ◽  
Comparison Results ◽  
Preconditioned Iterative

M-(H-)matrices appear in many areas of science and engineering, for example, in the solution of the linear complementarity problem (LCP) in optimization theory and in the solution of large systems for real-time changes of data in fluid analysis in car industry. Classical (stationary) iterative methods used for the solution of linear systems have been shown to convergence for this class of matrices. In this paper, we present some comparison theorems on the preconditioned AOR iterative method for solving the linear system. Comparison results show that the rate of convergence of the preconditioned iterative method is faster than the rate of convergence of the classical iterative method. Meanwhile, we apply the preconditioner toH-matrices and obtain the convergence result. Numerical examples are given to illustrate our results.

Perceptions of Stuttering of Different Age Groups

2019 ◽  
Vol 4 (6) ◽  
pp. 1311-1315
Author(s):  
Sergey M. Kondrashov ◽  
John A. Tetnowski
Keyword(s):  
Age Groups ◽  
School Age Children ◽  
Clinical Implications ◽  
School Age ◽  
Fourth Edition ◽  
Self Perception ◽  
Behavioral Measures ◽  
Self Rating ◽  
Comparison Results ◽  
Subject Pool

Purpose The purpose of this study was to assess the perceptions of stuttering of school-age children who stutter and those of adults who stutter through the use of the same tools that could be commonly used by clinicians. Method Twenty-three participants across various ages and stuttering severity were administered both the Stuttering Severity Instrument–Fourth Edition (SSI-4; Riley, 2009 ) and the Wright & Ayre Stuttering Self-Rating Profile ( Wright & Ayre, 2000 ). Comparisons were made between severity of behavioral measures of stuttering made by the SSI-4 and by age (child/adult). Results Significant differences were obtained for the age comparison but not for the severity comparison. Results are explained in terms of the correlation between severity equivalents of the SSI-4 and the Wright & Ayre Stuttering Self-Rating Profile scores, with clinical implications justifying multi-aspect assessment. Conclusions Clinical implications indicate that self-perception and impact of stuttering must not be assumed and should be evaluated for individual participants. Research implications include further study with a larger subject pool and various levels of stuttering severity.

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