Adaptive Array Processing Unit Based on Direct Data Domain Least Square Approach Using Conjugate Gradient Method

One of the popular approaches in modifying the Conjugate Gradient (CG) Method is hybridization. In this paper, a new hybrid CG is introduced and its performance is compared to the classical CG method which are Rivaie-Mustafa-Ismail-Leong (RMIL) and Syarafina-Mustafa-Rivaie (SMR) methods. The proposed hybrid CG is evaluated as a convex combination of RMIL and SMR method. Their performance are analyzed under the exact line search. The comparison performance showed that the hybrid CG is promising and has outperformed the classical CG of RMIL and SMR in terms of the number of iterations and central processing unit per time.

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On three-term conjugate gradient method for optimization problems with applications on COVID-19 model and robotic motion control

Advances in Continuous and Discrete Models ◽

10.1186/s13662-021-03638-9 ◽

2022 ◽

Vol 2022 (1) ◽

Author(s):

Ibrahim Mohammed Sulaiman ◽

Maulana Malik ◽

Aliyu Muhammed Awwal ◽

Poom Kumam ◽

Mustafa Mamat ◽

...

Keyword(s):

Regression Model ◽

Motion Control ◽

Conjugate Gradient Method ◽

Conjugate Gradient ◽

Gradient Method ◽

Optimization Problems ◽

Least Square ◽

Optimization Models ◽

Inexact Line Search ◽

Novel Coronavirus

AbstractThe three-term conjugate gradient (CG) algorithms are among the efficient variants of CG algorithms for solving optimization models. This is due to their simplicity and low memory requirements. On the other hand, the regression model is one of the statistical relationship models whose solution is obtained using one of the least square methods including the CG-like method. In this paper, we present a modification of a three-term conjugate gradient method for unconstrained optimization models and further establish the global convergence under inexact line search. The proposed method was extended to formulate a regression model for the novel coronavirus (COVID-19). The study considers the globally infected cases from January to October 2020 in parameterizing the model. Preliminary results have shown that the proposed method is promising and produces efficient regression model for COVID-19 pandemic. Also, the method was extended to solve a motion control problem involving a two-joint planar robot.

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Conjugate gradient method with graphics processing unit acceleration: CUDA vs OpenCL

Advances in Engineering Software ◽

10.1016/j.advengsoft.2016.10.002 ◽

2017 ◽

Vol 111 ◽

pp. 32-42 ◽

Cited By ~ 6

Author(s):

Abal-Kassim Cheik Ahamed ◽

Frédéric Magoulès

Keyword(s):

Conjugate Gradient Method ◽

Conjugate Gradient ◽

Gradient Method ◽

Graphics Processing Unit ◽

Processing Unit ◽

Graphics Processing

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Estimating the unemployment rate using least square and conjugate gradient methods

International Journal of Engineering & Technology ◽

10.14419/ijet.v7i2.15.11360 ◽

2018 ◽

Vol 7 (2.15) ◽

pp. 94

Author(s):

Nur Syarafina Mohamed ◽

Mustafa Mamat ◽

Mohd Rivaie ◽

Nur Hamizah Abdul Ghani ◽

Norhaslinda Zull ◽

...

Keyword(s):

Conjugate Gradient Method ◽

Unemployment Rate ◽

Conjugate Gradient ◽

Gradient Method ◽

Labour Force ◽

Gradient Methods ◽

Least Square Method ◽

Least Square ◽

Year 2000 ◽

Quadratic Models

Unemployment rate is one of the major issues among Malaysian citizens. The unemployment rate indicates the percentage of the total workforce who are actively seeking employment and currently unemployed. In this paper, a data of unemployment rate of a state in Malaysia from year 2000 until 2015 is collected. The statistics data is extracted by Labour Force Survey Malaysia (LFSM) which was conducted monthly by using household approach targeted to working ages between 15 to 64 years old. An estimation data for year 2016 can be forecasted by using discrete least square method of numerical analysis and conjugate gradient method in unconstrained optimization. These methods have been chosen based on its simplicity and accuracy. The calculations are based on linear and quadratic models for each the method together with their errors. Results showed that the conjugate gradient method is comparable with the least square method.

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A Convex Combination between Two Different Search Directions of Conjugate Gradient Method and Application in Image Restoration

Mathematical Problems in Engineering ◽

10.1155/2021/9941757 ◽

2021 ◽

Vol 2021 ◽

pp. 1-15

Author(s):

Ahmad Alhawarat ◽

Zabidin Salleh ◽

Ibtisam A. Masmali

Keyword(s):

Image Restoration ◽

Conjugate Gradient Method ◽

Conjugate Gradient ◽

Gradient Method ◽

Optimization Problems ◽

Convex Combination ◽

Small Scale ◽

Processing Unit ◽

Sufficient Descent Condition ◽

Search Directions

The conjugate gradient is a useful tool in solving large- and small-scale unconstrained optimization problems. In addition, the conjugate gradient method can be applied in many fields, such as engineering, medical research, and computer science. In this paper, a convex combination of two different search directions is proposed. The new combination satisfies the sufficient descent condition and the convergence analysis. Moreover, a new conjugate gradient formula is proposed. The new formula satisfies the convergence properties with the descent property related to Hestenes–Stiefel conjugate gradient formula. The numerical results show that the new search direction outperforms both two search directions, making it convex between them. The numerical result includes the number of iterations, function evaluations, and central processing unit time. Finally, we present some examples about image restoration as an application of the proposed conjugate gradient method.

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