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 An improved symmetric SOR iterative method for augmented systems

2012 ◽  
Vol 43 (4) ◽  
pp. 479-490 ◽  
Author(s):  
Davod Khojasteh Salkuyeh ◽  
Somayyeh Shamsi ◽  
Amir Sadeghi
Keyword(s):  
Iterative Method ◽  
Numerical Experiments ◽  
Convergence Properties ◽  
Augmented Systems

In this paper, the improved symmetric SOR (ISSOR) iterative method is introduced to solve augmented systems. Convergence properties of the proposed method are studied. Some numerical experiments of the ISSOR method are given to compare with that of the well-known SOR-like and MSSOR methods.

scholarly journals An efficient algorithm for estimating the parameters of superimposed exponential signals in multiplicative and additive noise

2013 ◽  
Vol 23 (1) ◽  
pp. 117-129 ◽  
Author(s):  
Jiawen Bian ◽  
Huiming Peng ◽  
Jing Xing ◽  
Zhihui Liu ◽  
Hongwei Li
Keyword(s):  
Parameter Estimation ◽  
Convergence Rate ◽  
Efficient Algorithm ◽  
Numerical Experiments ◽  
Additive Noise ◽  
Mean Squared Errors ◽  
Least Squares Estimators ◽  
The Mean ◽  
Newton Raphson ◽  
Raphson Algorithm

This paper considers parameter estimation of superimposed exponential signals in multiplicative and additive noise which are all independent and identically distributed. A modified Newton-Raphson algorithm is used to estimate the frequencies of the considered model, which is further used to estimate other linear parameters. It is proved that the modified Newton- Raphson algorithm is robust and the corresponding estimators of frequencies attain the same convergence rate with Least Squares Estimators (LSEs) under the same noise conditions, but it outperforms LSEs in terms of the mean squared errors. Finally, the effectiveness of the algorithm is verified by some numerical experiments.

Computational Models of Bio Heuristics Based on Physical and Cognitive Processes (Review)

2021 ◽  
Vol 27 (11) ◽  
pp. 563-574
Author(s):  
V. V. Kureychik ◽  
◽  
S. I. Rodzin ◽  
Keyword(s):  
Computational Complexity ◽  
Convergence Rate ◽  
Rate Of Convergence ◽  
Cognitive Processes ◽  
Computational Models ◽  
Optimization Problems ◽  
Search Space ◽  
Experimental Results ◽  
Software Implementation ◽  
Minimum Total Length

Computational models of bio heuristics based on physical and cognitive processes are presented. Data on such characteristics of bio heuristics (including evolutionary and swarm bio heuristics) are compared.) such as the rate of convergence, computational complexity, the required amount of memory, the configuration of the algorithm parameters, the difficulties of software implementation. The balance between the convergence rate of bio heuristics and the diversification of the search space for solutions to optimization problems is estimated. Experimental results are presented for the problem of placing Peco graphs in a lattice with the minimum total length of the graph edges.

A Filtered-Davidson Method for Large Symmetric Eigenvalue Problems

2017 ◽  
Vol 7 (1) ◽  
pp. 21-37 ◽  
Author(s):  
Cun-Qiang Miao
Keyword(s):  
Convergence Rate ◽  
Chebyshev Polynomials ◽  
Numerical Experiments ◽  
Eigenvalue Problems ◽  
Cubic Convergence ◽  
Davidson Method ◽  
Filtering Technique ◽  
Matrix Vector ◽  
Three Term Recurrence Relation ◽  
Symmetric Eigenvalue Problems

AbstractFor symmetric eigenvalue problems, we constructed a three-term recurrence polynomial filter by means of Chebyshev polynomials. The new filtering technique does not need to solve linear systems and only needs matrix-vector products. It is a memory conserving filtering technique for its three-term recurrence relation. As an application, we use this filtering strategy to the Davidson method and propose the filtered-Davidson method. Through choosing suitable shifts, this method can gain cubic convergence rate locally. Theory and numerical experiments show the efficiency of the new filtering technique.

A Fuzzy Adaptive K-SVD Dictionary Algorithm for Face Recogntion

2013 ◽  
Vol 347-350 ◽  
pp. 3797-3803 ◽  
Author(s):  
Xiao Ning Song ◽  
Zi Liu
Keyword(s):  
Iterative Method ◽  
Fuzzy Set ◽  
Sparse Coding ◽  
Sparse Representations ◽  
Experimental Results ◽  
Sparse Signal ◽  
Signal Representations ◽  
The Given ◽  
Class Assignment ◽  
Fuzzy Adaptive

Sparse representations using overcomplete dictionaries has concentrated mainly on the study of pursuit algorithms that decompose signals with respect to a given dictionary. Designing dictionaries to better fit the above model can be done by either selecting one from a prespecified set of linear transforms or adapting the dictionary to a set of training signals. The K-SVD algorithm is an iterative method that alternates between sparse coding of the examples based on the current dictionary and a process of updating the dictionary atoms to better fit the data. However, the existing K-SVD algorithm is employed to dwell on the concept of a binary class assignment meaning that the multi-classes samples are assigned to the given classes definitely. The work proposed in this paper provides a novel fuzzy adaptive way to adapting dictionaries in order to achieve the fuzzy sparse signal representations, the update of the dictionary columns is combined with an update of the sparse representations by incorporated a new mechanism of fuzzy set, which is called fuzzy K-SVD. Experimental results conducted on the ORL and Yale face databases demonstrate the effectiveness of the proposed method.

The Elastohydrodynamic Problem Expressed in Terms of Extended Variational Formulation

1986 ◽  
Vol 108 (4) ◽  
pp. 557-564 ◽  
Author(s):  
Antonio Strozzi
Keyword(s):  
Convergence Rate ◽  
Variational Formulation ◽  
Numerical Experiments ◽  
Numerical Results ◽  
Lubricated Contacts ◽  
Relaxation Scheme

The elastohydrodynamic problem is revisited in terms of an extended variational formulation, where the corresponding functional exhibits minimum properties in the solution neighborhood. Such features are exploited in the development of a relaxation-type solver. The numerical results indicate that the convergence rate of the proposed relaxation scheme becomes increasingly poor as the solution of the elastohydrodynamic problem is approached. A polyalgorithm based on a combination between relaxation-type and Newton-type schemes is proposed. The numerical experiments referred to various sealing profiles of increasing foundation compliance show that the proposed procedure is particularly advantageous in the case of soft lubricated contacts.

A New Preconditioned Generalised AOR Method for the Linear Complementarity Problem Based on a Generalised Hadjidimos Preconditioner

2012 ◽  
Vol 2 (2) ◽  
pp. 94-107 ◽  
Author(s):  
Cuiyu Liu ◽  
Chenliang Li
Keyword(s):  
Convergence Rate ◽  
Linear Complementarity Problem ◽  
Complementarity Problem ◽  
Numerical Experiments ◽  
Linear Complementarity ◽  
New Method ◽  
Aor Method

AbstractA new generalised Hadjidimos preconditioner and preconditioned generalised AOR method for the solution of the linear complementarity problem are presented. The convergence and convergence rate of the new method are analysed, and numerical experiments demonstrate that it is efficient.

Using Q-Learning and Genetic Algorithms to Improve the Efficiency of Weight Adjustments for Optimal Control and Design Problems

2005 ◽  
Author(s):  
Kaivan Kamali ◽  
Lijun Jiang ◽  
John Yen ◽  
K. W. Wang
Keyword(s):  
Optimal Control ◽  
Genetic Algorithms ◽  
Convergence Rate ◽  
Cost Function ◽  
Design Problem ◽  
Numerical Experiments ◽  
Design Parameters ◽  
Design Problems ◽  
Q Learning ◽  
Layered Approach

In traditional optimal control and design problems, the control gains and design parameters are usually derived to minimize a cost function reflecting the system performance and control effort. One major challenge of such approaches is the selection of weighting matrices in the cost function, which are usually determined via trial and error and human intuition. While various techniques have been proposed to automate the weight selection process, they either can not address complex design problems or suffer from slow convergence rate and high computational costs. We propose a layered approach based on Q-learning, a reinforcement learning technique, on top of genetic algorithms (GA) to determine the best weightings for optimal control and design problems. The layered approach allows for reuse of knowledge. Knowledge obtained via Q-learning in a design problem can be used to speed up the convergence rate of a similar design problem. Moreover, the layered approach allows for solving optimizations that cannot be solved by GA alone. To test the proposed method, we perform numerical experiments on a sample active-passive hybrid vibration control problem, namely adaptive structures with active-passive hybrid piezoelectric networks (APPN). These numerical experiments show that the proposed Q-learning scheme is a promising approach for.

scholarly journals Four-Point Optimal Sixteenth-Order Iterative Method for Solving Nonlinear Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Malik Zaka Ullah ◽  
A. S. Al-Fhaid ◽  
Fayyaz Ahmad
Keyword(s):  
Iterative Method ◽  
Nonlinear Equations ◽  
Numerical Experiments ◽  
Order Of Convergence ◽  
Iterative Scheme ◽  
Optimal Order ◽  
Optimal Order Of Convergence

We present an iterative method for solving nonlinear equations. The proposed iterative method has optimal order of convergence sixteen in the sense of Kung-Traub conjecture (Kung and Traub, 1974); it means that the iterative scheme uses five functional evaluations to achieve 16(=25-1) order of convergence. The proposed iterative method utilizes one derivative and four function evaluations. Numerical experiments are made to demonstrate the convergence and validation of the iterative method.

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