• 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.

• Kyungpook Mathematical Journal
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• v.55 no.3
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• pp.695-703
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• 2015

Several interesting and useful extensions of some familiar special functions such as Beta and Gauss hypergeometric functions and their properties have, recently, been investigated by many authors. Motivated mainly by those earlier works, we establish some fractional integral formulas involving the extended generalized Gauss hypergeometric function by using certain general pair of fractional integral operators involving Gauss hypergeometric function $_2F_1$, Some interesting special cases of our main results are also considered.

• Journal of the Korean Mathematical Society
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• v.53 no.6
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• pp.1309-1330
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• 2016

As a generalizing certain geometric property occurred on the helicoid of 3-dimensional Euclidean space regarding the Gauss map, we study ruled submanifolds in a Euclidean space with pointwise 1-type Gauss map of the first kind. In this paper, as new examples of cylindrical ruled submanifolds in Euclidean space, we construct generalized circular cylinders and characterize such ruled submanifolds and minimal ruled submanifolds of Euclidean space with pointwise 1-type Gauss map of the first kind.

• Journal of the Korean Mathematical Society
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• v.56 no.2
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• pp.311-327
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• 2019

The aim of this paper is to extend the applicability of Gauss-Newton method for solving underdetermined nonlinear least squares problems in cases not covered before. The novelty of the paper is the introduction of a restricted convergence domain. We find a more precise location where the Gauss-Newton iterates lie than in earlier studies. Consequently the Lipschitz constants are at least as small as the ones used before. This way and under the same computational cost, we extend the local as well the semilocal convergence of Gauss-Newton method. The new developmentes are obtained under the same computational cost as in earlier studies, since the new Lipschitz constants are special cases of the constants used before. Numerical examples further justify the theoretical results.

• Communications of the Korean Mathematical Society
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• v.37 no.4
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• pp.1055-1072
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• 2022

Our aim is to establish certain image formulas of the (p, 𝜈)-extended Gauss' hypergeometric function F_p,𝜈(a, b; c; z) by using Saigo's hypergeometric fractional calculus (integral and differential) operators. Corresponding assertions for the classical Riemann-Liouville(R-L) and Erdélyi-Kober(E-K) fractional integral and differential operators are deduced. All the results are represented in terms of the Hadamard product of the (p, 𝜈)-extended Gauss's hypergeometric function F_p,𝜈(a, b; c; z) and Fox-Wright function _rΨ_s(z). We also established Jacobi and its particular assertions for the Gegenbauer and Legendre transforms of the (p, 𝜈)-extended Gauss' hypergeometric function F_p,𝜈(a, b; c; z).

• Kyungpook Mathematical Journal
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• v.62 no.1
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• pp.167-177
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• 2022

In this manuscript, we handle a tubular surface whose Gauss map G satisfies the equality L₁G = f(G + C) for the Cheng-Yau operator L₁ in Galilean 3-space 𝔾₃. We give an example of a tubular surface having L₁-harmonic Gauss map. Moreover, we obtain a complete classification of tubular surface having L₁-pointwise 1-type Gauss map of the first kind in 𝔾₃ and we give some visualizations of this type surface.

• 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. 

• Transactions of the Korean Society of Mechanical Engineers
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• v.15 no.2
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• pp.445-454
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• 1991

In this thesis, Mindlin plate element with nine nodes and three degrees-of-freedom at each node is formulated and is employed in eigen-analysis of a rectangular plates in order to alleviate locking phenomenon of eigenvalues. Eigenvalues and their modes may be locked if conventional $C_{0}$-isoparametric element is used. In order to reduce stiffness locking phenomenon, two methods (1, the general reduced and selective integration, 2, the new element that use of modified shape function) are studied. Additionally in order to reduce the error due to mass matrix, two mass matrixes (1, Gauss-Legendre mass matrix, 2, Gauss-Lobatto mass matrix) are considered. The results of eigen-analysis for two models (the square plate with all edges simply-supported and all edges built-in), computed by two methods for stiffness matrix and by two mass matrixes are compared with theoretical solutions and conventional numerical solutions. These comparisons show that the performance of the two methods with Gauss-Lobatto mass matrix is better than that of the conventional plate element. But, by considering the spurious rigid body motions, the element which employs modified shape function with full integration and Gauss-Lobatto mass matrix can elevate the accuracy and convergence of numerical solutions.

• Journal of the Institute of Electronics and Information Engineers
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• v.52 no.8
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• pp.148-155
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• 2015

The Levenberg-Marquardt method is a well known solution about the least square problem. However, in a Target Motion Analysis(TMA) application most of researches have used the Gauss-Newton method as a batch estimator, which of inverse matrix calculation may causes instability problem. In this paper, Levenberg-Marquardt method is applied to TMA problem to prevent its divergence. In experiment, its performance is compared with Gauss-Newton in domain of range, course and speed. Monte Carlo simulation reveals the convergence time and reliability of the TMA based on Levenberg-Marquardt.

• Ocean Systems Engineering
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• v.7 no.4
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• pp.399-412
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• 2017

The Gauss-Legendre integral method is applied to numerically evaluate the Green function and its derivatives in finite water depth. In this method, the singular point of the function in the traditional integral equation can be avoided. Moreover, based on the improved Gauss-Laguerre integral method proposed in the previous research, a new methodology is developed through the Gauss-Legendre integral. Using this new methodology, the Green function with the field and source points near the water surface can be obtained, which is less mentioned in the previous research. The accuracy and efficiency of this new method is investigated. The numerical results using a Gauss-Legendre integral method show good agreements with other numerical results of direct calculations and series form in the far field. Furthermore, the cases with the field and source points near the water surface are also considered. Considering the computational efficiency, the method using the Gauss-Legendre integral proposed in this paper could obtain the accurate numerical results of the Green function and its derivatives in finite water depth and can be adopted in the near field.