• Bulletin of the Korean Mathematical Society
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• v.48 no.2
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• pp.303-314
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• 2011

For Ax = b, it has recently been reported that the convergence of the preconditioned Gauss-Seidel iterative method which uses a matrix of the type P = I + S (${\alpha}$) to perform certain elementary row operations on is faster than the basic Gauss-Seidel method. In this paper, we discuss the adaptive Gauss-Seidel iterative method which uses P = I + S (${\alpha}$) + $\bar{K}({\beta})$ as a preconditioner. We present some comparison theorems, which show the rate of convergence of the new method is faster than the basic method and the method in [7] theoretically. Numerical examples show the effectiveness of our algorithm.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.41 no.2
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• pp.117-124
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• 2017

The performance of the colored Gauss-Seidel solver on CPU and GPU was investigated for the two- and three-dimensional heat conduction problems by using different mesh sizes. The heat conduction equation was discretized by the finite difference method and finite element method. The CPU yielded good performance for small problems but deteriorated when the total memory required for computing was larger than the cache memory for large problems. In contrast, the GPU performed better as the mesh size increased because of the latency hiding technique. Further, GPU computation by the colored Gauss-Siedel solver was approximately 7 times that by the single CPU. Furthermore, the colored Gauss-Seidel solver was found to be approximately twice that of the Jacobi solver when parallel computing was conducted on the GPU.

• Communications of the Korean Mathematical Society
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• v.28 no.3
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• pp.603-613
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• 2013

In 2009, Zheng and Miao [B. Zheng and S.-X. Miao, Two new modified Gauss-Seidel methods for linear system with M-matrices, J. Comput. Appl. Math. 233 (2009), 922-930] considered the modified Gauss-Seidel method for solving M-matrix linear system with the preconditioner $P_{max}$. In this paper, we consider the modified Gauss-Seidel method for solving the linear system with the generalized preconditioner $P_{max}({\alpha})$, and study its convergent properties when the coefficient matrix is an H-matrix. Numerical experiments are performed with different examples, and the numerical results verify our theoretical analysis.

• Journal of the Institute of Electronics Engineers of Korea TE
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• v.39 no.3
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• pp.15-20
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• 2002

In this paper, the method of processing a blurred noisy signal has been researched. The conventional method of processing signal has faults, which are slow-convergence speed and long time-consuming process at the singular point and/or in the ill condition. There is the process, the Gauss-Seidel's method to remove these faults, but it takes too much time because it processes signal repeatedly. For overcoming the faults, this paper shows a signal process method which takes shorter than the Gauss-Seidel's by comparing the Gauss-Seidel's with proposed algorithm and accelerating convergence speed at the singular point and/or in the ill condition. 

• Communications of the Korean Mathematical Society
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• v.27 no.1
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• pp.207-215
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• 2012

In this paper, we provide comparison results of several types of the preconditioned Gauss-Seidel methods for solving a linear system whose coefficient matrix is a Z-matrix. Lastly, numerical results are presented to illustrate the theoretical results.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.19 no.10
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• pp.2001-2013
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• 1994

In this paper, the method of processing a blurred noisy image has been researched. The conventional method of processing signal has faluts which are slow convergence speed and long time-consuming process at the singular point and or in the ill condition. There is the process, the Gauss Seidel's method to remove these faults, but it takes too much time because it processed singnal repeatedly. For overcoming the faults, this paper shows a image restoration method which takes shorter than the Gauss-Seidel's by comparing the Gauss Seidel's with proposed alogorithm and accelerating convergence speed at the singular point and/or in the ill condition. In this paper, the conventional process method(Gauss-Seidel) and proposed optimal algorithm were used to get a standard image($256{\times}56{\times}bits$). and then the results are simulated and compared each other in order to examine the variance of MSE(Mean Square Error) by the acceleration parameter in the proposed image restoration. The result of the signal process and the process time was measured at all change of acceleration parameter in order to verify the effectveness of the proposed algorithm.

• Journal of applied mathematics & informatics
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• v.25 no.1_2
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• pp.119-136
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• 2007

Block Jacobi and Gauss-Seidel iterative methods are studied for solving $n{\times}n$ fuzzy linear systems. A new splitting method is considered as well. These methods are accompanied with some convergence theorems. Numerical examples are presented to illustrate the theory.

• 한국전산유체공학회:학술대회논문집
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• 2001.05a
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• pp.93-98
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• 2001

An adaptive Cartesian grid method having the best elements of structured, unstructured, and Cartesian grids is developed to solve the steady two-dimensional Euler equations. The solver is based on a cell-centered finite-volume method with Roe's flux-difference splitting and implicit point Gauss-seidel time integration method. Calculations of several compressible flows are carried out to show the efficiency of the developed computer code. The results were generally in good agreements with existing data in the literature and the developed code has the good ability to capture important feature of the flows.

• Journal of Broadcast Engineering
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• v.27 no.2
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• pp.244-247
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• 2022

In this paper, the performance of the decoding schemes using linear MMSE filters in the frequency and time domains and the reinforcement Gauss-Seidel algorithm for the orthogonal time frequency space (OTFS) system that can improve robustness under high-speed mobile environments are compared. The reinforcement Gauss-Seidel algorithm can improve the bit error rate performance by suppressing the noise enhancement. The simulation results show that the performance of the decoding scheme using the linear MMSE filter in the frequency domain is severely degraded due to the effect of Doppler shift as the mobile speed increases. In addition, the decoding scheme using the reinforcement Gauss-Seidel algorithm under the channel environment with 120 km/h and 500 km/h speeds outperforms the decoding schemes using linear MMSE filters in the frequency and time domains.

• The KSFM Journal of Fluid Machinery
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• v.6 no.1 s.18
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• pp.44-50
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• 2003

Flow through a turbine flow meter is simulated by solving the incompressible Navier-Stokes equations. The solution method is based on the pseudo-compressibility approach and uses an implicit-upwind differencing scheme together with the Gauss-Seidel line relaxation method. The equations are solved steadily in rotating reference frames, and the centrifugal force and the Coriolis force are added to the equation of motion. The standard $k-{\epsilon}$model is employed to evaluate turbulent viscosity. Computational results yield quantitative as well as qualitative information on the design of turbine flow meters by showing the distributions of pressure and velocity around the turbine blades.