Convergence rate of iterative method for problem with free phase in case of isometric operator

2004 ◽  
Author(s):  
Yu.P. Topolyuk ◽  
N.N. Voitovich
Keyword(s):  
Convergence Rate ◽  
Iterative Method ◽  
Isometric Operator

scholarly journals Iterative method for solving the second boundary value problem (BVP) for Biharmonic type equation

2016 ◽  
Vol 14 (4) ◽  
pp. 66-72
Author(s):  
Đặng Quang Á
Keyword(s):  
Differential Equations ◽  
Convergence Rate ◽  
Iterative Method ◽  
Boundary Value Problem ◽  
Fourth Order ◽  
Boundary Value ◽  
Type Equation ◽  
Second Order ◽  
Second Order Equations

Solving BVPs for the fourth order differential equations by the reduction of them to BVPs for the  second order equations with the aim to use the achievements for the latter ones attracts attention from many researchers. In this paper, using the technique developed by  ourselves in recent works, we construct iterative method for the second BVP for  biharmonic type equation. The convergence rate of  the method is established.

scholarly journals An iterative method to compute Moore-Penrose inverse based on gradient maximal convergence rate

Filomat ◽  
2013 ◽  
Vol 27 (7) ◽  
pp. 1269-1276 ◽  
Author(s):  
Xingping Sheng ◽  
Tao Wang
Keyword(s):  
Convergence Rate ◽  
Iterative Method ◽  
Computation Time ◽  
The Other ◽  
Singular Matrix ◽  
Initial Matrix ◽  
Numerical Example

In this paper, we present an iterative method based on gradient maximal convergence rate to compute Moore-Penrose inverse A+ of a given matrix A. By this iterative method, when taken the initial matrix X0 = A*, the M-P inverse A+ can be obtained with maximal convergence rate in absence of round off errors. In the end, a numerical example is given to illustrate the effectiveness, accuracy and its computation time, which are all superior than the other methods for the large singular matrix.

scholarly journals Convergence of a Generalized USOR Iterative Method for Augmented Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Yu-Qin Bai ◽  
Ting-Zhu Huang ◽  
Miao-Miao Yu
Keyword(s):  
Convergence Rate ◽  
Iterative Method ◽  
Numerical Experiments ◽  
Experimental Results ◽  
Augmented Systems ◽  
Iteration Parameters

Zhang and Shang (2010) have presented the Uzawa-SOR (USOR) algorithm to solve augmented systems. In this paper, we establish a generalized Uzawa-SOR (GUSOR) method for solving augmented systems, which is the extension of the USOR method. We prove the convergence of the proposed method under suitable restrictions on the iteration parameters. Lastly, numerical experiments are carried out and experimental results show that our proposed method with appropriate parameters has faster convergence rate than the USOR method.

scholarly journals Iterative Method for Solving the Second Boundary Value Problem for Biharmonic-Type Equation

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
Dang Quang A. ◽  
Nguyen Van Thien
Keyword(s):  
Differential Equations ◽  
Convergence Rate ◽  
Iterative Method ◽  
Boundary Value Problem ◽  
Fourth Order ◽  
Boundary Value ◽  
Type Equation ◽  
Numerical Examples ◽  
Optimal Value ◽  
Second Order Equations

Solving boundary value problems (BVPs) for the fourth-order differential equations by the reduction of them to BVPs for the second-order equations with the aim to use the achievements for the latter ones attracts attention from many researchers. In this paper, using the technique developed by ourselves in recent works, we construct iterative method for the second BVP for biharmonic-type equation, which describes the deflection of a plate resting on a biparametric elastic foundation. The convergence rate of the method is established. The optimal value of the iterative parameter is found. Several numerical examples confirm the efficiency of the proposed method.

scholarly journals An optimized AOR iterative method for solving absolute value equations

Filomat ◽  
2021 ◽  
Vol 35 (2) ◽  
pp. 459-476
Author(s):  
Alireza Fakharzadeh Jahromi ◽  
Nafiseh Shamsa
Keyword(s):  
Convergence Rate ◽  
Iterative Method ◽  
Optimization Techniques ◽  
Optimal Parameters ◽  
Absolute Value Equations ◽  
Absolute Value ◽  
Sor Methods ◽  
Two Parameters

In recent years, the AOR iterative method has been proposed for solving absolute value equations. This method has two parameters ? and ?. In this paper, we intend to find the optimal parameters of this method to improve convergence rate by suitable optimization techniques. Meanwhile, the convergence of the optimized AOR iterative method is discussed. It is both theoretically and experimentally demonstrated efficiency of the optimized AOR iterative method in contrast with the AOR and SOR methods.

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.

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