Note To The Mixed-Type Splitting Iterative Method For The Positive Real Linear System

2002 ◽  
Vol 79 (11) ◽  
pp. 1201-1209 ◽  
Author(s):  
Changjun Li ◽  
David Evans
Keyword(s):  
Linear System ◽  
Iterative Method ◽  
Mixed Type ◽  
Positive Real ◽  
Real Linear

An iterative method for the positive real linear system

2001 ◽  
Vol 78 (1) ◽  
pp. 153-163 ◽  
Author(s):  
Li Changjun ◽  
Liang Xiaoli ◽  
David Evans
Keyword(s):  
Linear System ◽  
Iterative Method ◽  
Positive Real ◽  
Real Linear

scholarly journals Some Results on Preconditioned Mixed-Type Splitting Iterative Method

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Guangbin Wang ◽  
Fuping Tan
Keyword(s):  
Linear System ◽  
Iterative Method ◽  
Rate Of Convergence ◽  
Mixed Type ◽  
Comparison Theorems ◽  
Numerical Example

We present a preconditioned mixed-type splitting iterative method for solving the linear system Ax=b, where A is a Z-matrix. And we give some comparison theorems to show that the rate of convergence of the preconditioned mixed-type splitting iterative method is faster than that of the mixed-type splitting iterative method. Finally, we give one numerical example to illustrate our results.

scholarly journals A Modification of Minimal Residual Iterative Method to Solve Linear Systems

2009 ◽  
Vol 2009 ◽  
pp. 1-9 ◽  
Author(s):  
Xingping Sheng ◽  
Youfeng Su ◽  
Guoliang Chen
Keyword(s):  
Linear System ◽  
Iterative Method ◽  
Linear Systems ◽  
Residual Error ◽  
Projection Technique ◽  
Numerical Example ◽  
Minimal Residual

We give a modification of minimal residual iteration (MR), which is 1V-DSMR to solve the linear systemAx=b. By analyzing, we find the modifiable iteration to be a projection technique; moreover, the modification of which gives a better (at least the same) reduction of the residual error than MR. In the end, a numerical example is given to demonstrate the reduction of the residual error between the 1V-DSMR and MR.

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>

An optimum iterative method for solving any linear system with a square matrix

1988 ◽  
Vol 28 (1) ◽  
pp. 163-178 ◽  
Author(s):  
Dennis C. Smolarski ◽  
Paul E. Saylor
Keyword(s):  
Linear System ◽  
Iterative Method ◽  
Square Matrix

THE BANACH-LIE *-ALGEBRA OF MULTIPLICATION OPERATORS ON A W*-ALGEBRA

2011 ◽  
Vol 04 (02) ◽  
pp. 235-261
Author(s):  
Maysaa Alqurashi ◽  
Najla A. Altwaijry ◽  
C. Martin Edwards ◽  
Christopher S. Hoskin
Keyword(s):  
State Space ◽  
Lie Algebra ◽  
The State ◽  
Multiplication Operators ◽  
Dual Cone ◽  
Positive Real ◽  
Linear Isometry ◽  
Real Linear ◽  
Special Case

The hermitian part [Formula: see text] of the Banach-Lie *-algebra [Formula: see text] of multiplication operators on the W *-algebra A is a unital GM-space, the base of the dual cone in the dual GL-space [Formula: see text] of which is affine isomorphic and weak*-homeomorphic to the state space of [Formula: see text]. It is shown that there exists a Lie *-isomorphism ϕ from the quotient (A ⊕∞ Aop)/K of an enveloping W *-algebra A ⊕∞ Aop of A by a weak*-closed Lie *-ideal K onto [Formula: see text], the restriction to the hermitian part ((A ⊕∞ Aop)/K)h of which is a bi-positive real linear isometry, thereby giving a characterization of the state space of [Formula: see text]. In the special case in which A is a W *-factor this leads to a further identification of the state space of [Formula: see text] in terms of the state space of A. For any W *-algebra A, the Banach-Lie *-algebra [Formula: see text] coincides with the set of generalized derivations of A, and, as an application, a formula is obtained for the norm of an element of [Formula: see text] in terms of a centre-valued 'norm' on A, which is similar to that previously obtained by non-order-theoretic methods.

scholarly journals Note to the mixed-type splitting iterative method for Z-matrices linear systems

2008 ◽  
Vol 220 (1-2) ◽  
pp. 1-7 ◽  
Author(s):  
Guang-Hui Cheng ◽  
Ting-Zhu Huang ◽  
Shu-Qian Shen
Keyword(s):  
Iterative Method ◽  
Linear Systems ◽  
Mixed Type

Convergence of the Preconditioned AOR Method for an H-Matrix

2013 ◽  
Vol 756-759 ◽  
pp. 2615-2619
Author(s):  
Jie Jing Liu
Keyword(s):  
Linear System ◽  
Iterative Method ◽  
Numerical Experiments ◽  
Convergence Rates ◽  
Triangular Matrix ◽  
Coefficient Matrix ◽  
Aor Method ◽  
Upper Triangular Matrix ◽  
Theoretical Results

Linear system with H-matrix often appears in a wide variety of areas and is studied by many numerical researchers. In order to improve the convergence rates of iterative method solving the linear system whose coefficient matrix is an H-matrix. In this paper, a preconditioned AOR iterative method with a multi-parameters preconditioner with a general upper triangular matrix is proposed. In addition, the convergence of the coressponding iterative method are established. Lastly, we provide numerical experiments to illustrate the theoretical results.

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