scholarly journals Second Degree Generalized Successive Over Relaxation Method for Solving System of Linear Equations

2020 ◽  
Vol 12 (1) ◽  
pp. 60-71
Author(s):  
Firew Hailu ◽  
Genanew Gofe Gonfa ◽  
Hailu Muleta Chemeda
Keyword(s):  
Iterative Method ◽  
Linear Equations ◽  
Relaxation Method ◽  
The Other ◽  
System Of Linear Equations ◽  
Convergence Properties ◽  
Numerical Examples ◽  
Successive Over Relaxation ◽  
Number Of Iterations ◽  
Second Degree

In this paper, a second degree generalized successive over relaxation iterative method for solving system of linear equations based on the decomposition  A= Dm+Lm+Um  is presented and the convergence properties of the proposed method are discussed. Two numerical examples are considered to show the efficiency of the proposed method. The results presented in tables show that the Second Degree Generalized Successive Over Relaxation Iterative method is more efficient than the other methods considered based on number of iterations, computational running time and accuracy. Keywords: Second Degree, Generalized Gauss Seidel, Successive over relaxation, Convergence.

scholarly journals Hybrid Bernstein Block-Pulse Functions Method for Second Kind Integral Equations with Convergence Analysis

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Mohsen Alipour ◽  
Dumitru Baleanu ◽  
Fereshteh Babaei
Keyword(s):  
Integral Equation ◽  
Approximate Solution ◽  
Convergence Analysis ◽  
Bernstein Polynomials ◽  
Linear Equations ◽  
The Other ◽  
New Combination ◽  
System Of Linear Equations ◽  
Numerical Examples ◽  
Block Pulse Functions

We introduce a new combination of Bernstein polynomials (BPs) and Block-Pulse functions (BPFs) on the interval [0, 1]. These functions are suitable for finding an approximate solution of the second kind integral equation. We call this method Hybrid Bernstein Block-Pulse Functions Method (HBBPFM). This method is very simple such that an integral equation is reduced to a system of linear equations. On the other hand, convergence analysis for this method is discussed. The method is computationally very simple and attractive so that numerical examples illustrate the efficiency and accuracy of this method.

scholarly journals Second degree generalized Jacobi iteration method for solving system of linear equations

2016 ◽  
Vol 47 (2) ◽  
pp. 179-192
Author(s):  
Tesfaye Kebede Enyew
Keyword(s):  
Spectral Radius ◽  
Iteration Method ◽  
Linear Equations ◽  
System Of Linear Equations ◽  
Numerical Examples ◽  
Jacobi Iteration ◽  
Optimal Values ◽  
Second Degree

In this paper, a Second degree generalized Jacobi Iteration method for solving system of linear equations, $Ax=b$ and discuss about the optimal values $a_{1}$ and $b_{1}$ in terms of spectral radius about for the convergence of SDGJ method of $x^{(n+1)}=b_{1}[D_{m}^{-1}(L_{m}+U_{m})x^{(n)}+k_{1m}]-a_{1}x^{(n-1)}.$ Few numerical examples are considered to show that the effective of the Second degree Generalized Jacobi Iteration method (SDGJ) in comparison with FDJ, FDGJ, SDJ.

scholarly journals Refinement of Extended Accelerated Over-Relaxation Method for Solution of Linear Systems

2021 ◽  
Vol 4 (1) ◽  
pp. 53-61
Author(s):  
KJ Audu ◽  
YA Yahaya ◽  
KR Adeboye ◽  
UY Abubakar
Keyword(s):  
Spectral Radius ◽  
Linear Equations ◽  
Relaxation Method ◽  
System Of Linear Equations ◽  
Iteration Matrix ◽  
Diagonally Dominant Matrix ◽  
Diagonally Dominant ◽  
Dominant Matrix ◽  
Successive Over Relaxation ◽  
Stationary Iterative Methods

Given any linear stationary iterative methods in the form z^(i+1)=Jz^(i)+f, where J is the iteration matrix, a significant improvements of the iteration matrix will decrease the spectral radius and enhances the rate of convergence of the particular method while solving system of linear equations in the form Az=b. This motivates us to refine the Extended Accelerated Over-Relaxation (EAOR) method called Refinement of Extended Accelerated Over-Relaxation (REAOR) so as to accelerate the convergence rate of the method. In this paper, a refinement of Extended Accelerated Over-Relaxation method that would minimize the spectral radius, when compared to EAOR method, is proposed. The method is a 3-parameter generalization of the refinement of Accelerated Over-Relaxation (RAOR) method, refinement of Successive Over-Relaxation (RSOR) method, refinement of Gauss-Seidel (RGS) method and refinement of Jacobi (RJ) method. We investigated the convergence of the method for weak irreducible diagonally dominant matrix, matrix or matrix and presented some numerical examples to check the performance of the method. The results indicate the superiority of the method over some existing methods.

scholarly journals A Preconditioned Iteration Method for Solving Sylvester Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Jituan Zhou ◽  
Ruirui Wang ◽  
Qiang Niu
Keyword(s):  
Iterative Method ◽  
Iteration Method ◽  
Linear Equations ◽  
System Of Linear Equations ◽  
Newton's Iteration ◽  
Gradient Based ◽  
Selection Of

A preconditioned gradient-based iterative method is derived by judicious selection of two auxil- iary matrices. The strategy is based on the Newton’s iteration method and can be regarded as a generalization of the splitting iterative method for system of linear equations. We analyze the convergence of the method and illustrate that the approach is able to considerably accelerate the convergence of the gradient-based iterative method.

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>

scholarly journals Mechanical Analogy-based Iterative Method for Solving a System of Linear Equations

2015 ◽  
Vol 15 (08) ◽  
Author(s):  
Yuri Berchun ◽  
Pavel Burkov ◽  
Ayyyna Chirkova ◽  
Sayyyna Prokopieva ◽  
Dmitri Rabkin ◽  
...  
Keyword(s):  
Iterative Method ◽  
Linear Equations ◽  
System Of Linear Equations ◽  
Mechanical Analogy

A System of Linear Equations with an Infinity of Unknowns

1924 ◽  
Vol 22 (3) ◽  
pp. 282-286
Author(s):  
E. C. Titchmarsh
Keyword(s):  
Present Note ◽  
Linear Equations ◽  
The Other ◽  
System Of Linear Equations ◽  
Other Hand ◽  
Image Position ◽  
Monotonic Character

I have collected in the present note some theorems regarding the solution of a certain system of linear equations with an infinity of unknowns. The general form of the equations isthe numbers a1, a2, … c1, c2, … being given. Equations of this type are of course well known; but in studying them it is generally assumed that the series depend for convergence on the convergence-exponent of the sequences involved, e.g. that and are convergent. No assumptions of this kind are made here, and in fact the series need not be absolutely convergent. On the other hand rather special assumptions are made with regard to the monotonic character of the sequences an and cn.

scholarly journals Implementation of TAGE Method Using Seikkala Derivatives Applied to Two-Point Fuzzy Boundary Value Problems

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
A. A. Dahalan ◽  
J. Sulaiman
Keyword(s):  
Boundary Value Problems ◽  
Numerical Experiments ◽  
Boundary Value ◽  
Linear Equations ◽  
Alternating Group ◽  
System Of Linear Equations ◽  
Fuzzy Boundary Value Problems ◽  
Fuzzy Boundary ◽  
Two Parameter ◽  
Number Of Iterations

Iterative methods particularly the Two-Parameter Alternating Group Explicit (TAGE) methods are used to solve system of linear equations generated from the discretization of two-point fuzzy boundary value problems (FBVPs). The formulation and implementation of the TAGE method are also presented. Then numerical experiments are carried out onto two example problems to verify the effectiveness of the method. The results show that TAGE method is superior compared to GS method in the aspect of number of iterations, execution time, and Hausdorff distance.

scholarly journals On the simultaneous improving k inclusion disks for polynomial zeros

Filomat ◽  
2008 ◽  
Vol 22 (2) ◽  
pp. 9-21
Author(s):  
Dusan Milosevic ◽  
Miodrag Petkovic
Keyword(s):  
Iterative Method ◽  
Order Of Convergence ◽  
Convergence Properties ◽  
Polynomial Zeros ◽  
Numerical Examples ◽  
Modified Method

A modification of the iterative method of B?rsch-Supan type for the simultaneous inclusion of polynomial zeros is considered. The modified method provides the simultaneous inclusion of k (of n ? k) zeros, dealing with k inclusion disks of these zeros and the point (unchangeable) approximations to the remaining n - k zeros. It is proved that the R-order of convergence of the considered method is two if k < n and three if k = n. Three numerical examples are given to illustrate convergence properties of the presented method. .

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