Convergence of Matrix Relaxed Multisplitting USAOR Method

2014 ◽  
Vol 543-547 ◽  
pp. 1922-1925
Author(s):  
Yan Ping Wang ◽  
Li Tao Zhang
Keyword(s):  
Linear System ◽  
Iterative Methods ◽  
Coefficient Matrix ◽  
Sparse Linear System ◽  
Multisplitting Method ◽  
Convergent Rate

Relaxed technique is one of techniques for improving convergent rate of splitting iterative methods. In this paper,we study the convergence of both local relaxed parallel multisplitting method associated with USAOR multisplitting for solving a large sparse linear system whose coefficient matrix is anH-matrix.

scholarly journals Solutions of reaction-diffusion equations using similarity reduction and HSSOR iteration

2019 ◽  
Vol 16 (3) ◽  
pp. 1430
Author(s):  
Nur Afza Mat Ali ◽  
Rostang Rahman ◽  
Jumat Sulaiman ◽  
Khadizah Ghazali
Keyword(s):  
Differential Equation ◽  
Linear System ◽  
Iterative Method ◽  
Iterative Methods ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Sparse Linear System ◽  
Successive Over Relaxation ◽  
Number Of Iterations

<p>Similarity method is used in finding the solutions of partial differential equation (PDE) in reduction to the corresponding ordinary differential equation (ODE) which are not easily integrable in terms of elementary or tabulated functions. Then, the Half-Sweep Successive Over-Relaxation (HSSOR) iterative method is applied in solving the sparse linear system which is generated from the discretization process of the corresponding second order ODEs with Dirichlet boundary conditions. Basically, this ODEs has been constructed from one-dimensional reaction-diffusion equations by using wave variable transformation. Having a large-scale and sparse linear system, we conduct the performances analysis of three iterative methods such as Full-sweep Gauss-Seidel (FSGS), Full-sweep Successive Over-Relaxation (FSSOR) and HSSOR iterative methods to examine the effectiveness of their computational cost. Therefore, four examples of these problems were tested to observe the performance of the proposed iterative methods.  Throughout implementation of numerical experiments, three parameters have been considered which are number of iterations, execution time and maximum absolute error. According to the numerical results, the HSSOR method is the most efficient iterative method in solving the proposed problem with the least number of iterations and execution time followed by FSSOR and FSGS iterative methods.</p>

New Convergence of Relaxed Parallel Multisplitting Method for the H-Matrix

2013 ◽  
Vol 756-759 ◽  
pp. 3162-3166
Author(s):  
You Lin Zhang ◽  
Li Tao Zhang
Keyword(s):  
Linear System ◽  
Theoretical Analysis ◽  
Convergence Rate ◽  
Iterative Method ◽  
Coefficient Matrix ◽  
Convergence Domain ◽  
Multisplitting Method ◽  
Multisplitting Methods ◽  
Relaxed Multisplitting Method

Relaxed technique is one of the main techniques for Improving convergence rate of splitting iterative method. Based on existing parallel multisplitting methods, we have deeply studied the convergence of the relaxed multisplitting method associated with TOR multisplitting for solving the linear system whose coefficient matrix is an H-matrix. Moreover, theoretical analysis have shown that the convergence domain of the relaxed parameters is weaker and wider.

scholarly journals Parallelization of the solve phase in a task-based Cholesky solver using a sequential task flow model

2019 ◽  
Vol 34 (3) ◽  
pp. 340-356
Author(s):  
Sébastien Cayrols ◽  
Iain S Duff ◽  
Florent Lopez
Keyword(s):  
Linear System ◽  
Flow Model ◽  
State Of The Art ◽  
Direct Methods ◽  
Dramatic Reduction ◽  
Multicore Architecture ◽  
Sequential Task ◽  
Sparse Linear System ◽  
Parallel Version ◽  
Two Phases

We describe the parallelization of the solve phase in the sparse Cholesky solver SpLLT when using a sequential task flow model. In the context of direct methods, the solution of a sparse linear system is achieved through three main phases: the analyse, the factorization and the solve phases. In the last two phases, which involve numerical computation, the factorization corresponds to the most computationally costly phase, and it is therefore crucial to parallelize this phase in order to reduce the time-to-solution on modern architectures. As a consequence, the solve phase is often not as optimized as the factorization in state-of-the-art solvers, and opportunities for parallelism are often not exploited in this phase. However, in some applications, the time spent in the solve phase is comparable to or even greater than the time for the factorization, and the user could dramatically benefit from a faster solve routine. This is the case, for example, for a conjugate gradient (CG) solver using a block Jacobi preconditioner. The diagonal blocks are factorized once only, but their factors are used to solve subsystems at each CG iteration. In this study, we design and implement a parallel version of a task-based solve routine for an OpenMP version of the SpLLT solver. We show that we can obtain good scalability on a multicore architecture enabling a dramatic reduction of the overall time-to-solution in some applications.

scholarly journals H-Matrices in Fuzzy Linear Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
H. Saberi Najafi ◽  
S. A. Edalatpanah
Keyword(s):  
Linear System ◽  
Theoretical Analysis ◽  
Linear Systems ◽  
Numerical Experiments ◽  
Coefficient Matrix ◽  
System Of Equations ◽  
Linear System Of Equations ◽  
Fuzzy Linear System ◽  
Fuzzy Linear Systems

We consider a class of fuzzy linear system of equations and demonstrate some of the existing challenges. Furthermore, we explain the efficiency of this model when the coefficient matrix is an H-matrix. Numerical experiments are illustrated to show the applicability of the theoretical analysis.

Convergence analysis of the new splitting preconditioned SOR-type iterative methods for the linear system

2014 ◽  
Vol 30 (5) ◽  
pp. 1716-1726 ◽  
Author(s):  
Gang Lei ◽  
Jianhong Yang ◽  
Yihu Chen ◽  
Jianwei Yang ◽  
Jian Li
Keyword(s):  
Linear System ◽  
Convergence Analysis ◽  
Iterative Methods
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