• Journal of applied mathematics & informatics
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• 제5권2호
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• pp.383-392
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• 1998

This paper proposes Generalized Stationary Iterative called GSI method. It is shown that the existing stationary iterative methods are special cases of GSI method. Convergence properties of this method are provided and their numerical experiments for linear systems with symmetric positive definite matrix are also provided.

• 대한수학회논문집
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• 제28권3호
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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.

• 대한수학회지
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• 제49권5호
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• pp.927-945
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• 2012

An approximation of singular source terms in elliptic problems is developed and analyzed. Under certain assumptions on the curve where the singular source is defined, the second order convergence in the maximum norm can be proved. Numerical results present its better performance compared to previously developed regularization techniques.

• Communications for Statistical Applications and Methods
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• 제7권1호
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• pp.47-54
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• 2000

This article is concerned with the algorithm for the Chebyshev estimation with/without linear equality and/or inequality constraints. The algorithm employs a linear scaling transformation scheme to reduce the computational burden which is induced when the data set is quite large. The convergence of the proposed algorithm is proved. And the updating and orthogonal decomposition techniques are considered to improve the computational efficiency and numerical stability.

• 한국군사과학기술학회지
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• 제9권2호
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• pp.152-160
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• 2006

Time marching methods are well-suited for high speed compressible flow computations. However, it is well known that the time marching methods suffer a slow down in convergence due to disparity in Eigenvalues. A local preconditioning method is one of numerical methods to enhance convergence characteristics of low mach number flows by modifying Eigenvalues of the governing equations. In this paper, the local preconditioning method of Weiss is applied to a 2 dimensional Navier-Stokes code and the efficiency of the preconditioning method is shown through a number of computational examples.

• Journal of applied mathematics & informatics
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• 제29권5_6호
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• pp.1167-1178
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• 2011

In this paper, we further investigate the local Hermitian and skew-Hermitian splitting (LHSS) iteration method and the modified LHSS (MLHSS) iteration method for solving generalized nonsymmetric saddle point problems with nonzero (2,2) blocks. When A is non-symmetric positive definite, the convergence conditions are obtained, which generalize some results of Jiang and Cao [M.-Q. Jiang and Y. Cao, On local Hermitian and Skew-Hermitian splitting iteration methods for generalized saddle point problems, J. Comput. Appl. Math., 2009(231): 973-982] for the generalized saddle point problems to generalized nonsymmetric saddle point problems with nonzero (2,2) blocks. Numerical experiments show the effectiveness of the iterative methods.

• Nonlinear Functional Analysis and Applications
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• 제27권2호
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• pp.381-403
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• 2022

The main goal of this research is to solve variational inequalities involving quasimonotone operators in infinite-dimensional real Hilbert spaces numerically. The main advantage of these iterative schemes is the ease with which step size rules can be designed based on an operator explanation rather than the Lipschitz constant or another line search method. The proposed iterative schemes use a monotone and non-monotone step size strategy based on mapping (operator) knowledge as a replacement for the Lipschitz constant or another line search method. The strong convergences have been demonstrated to correspond well to the proposed methods and to settle certain control specification conditions. Finally, we propose some numerical experiments to assess the effectiveness and influence of iterative methods.

• 대한수학회지
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• 제50권6호
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• pp.1291-1310
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• 2013

This paper develops least-squares pseudo-spectral collocation methods for elliptic boundary value problems having interface conditions given by discontinuous coefficients and singular source term. From the discontinuities of coefficients and singular source term, we derive the interface conditions and then we impose such interface conditions to solution spaces. We define two types of discrete least-squares functionals summing discontinuous spectral norms of the residual equations over two sub-domains. In this paper, we show that the homogeneous least-squares functionals are equivalent to appropriate product norms and the proposed methods have the spectral convergence. Finally, we present some numerical results to provide evidences for analysis and spectral convergence of the proposed methods.

• Journal of applied mathematics & informatics
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• 제29권1_2호
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• pp.173-190
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• 2011

In this paper, we construct a new approach of affine scaling interior algorithm using the affine scaling conjugate gradient and Lanczos methods for bound constrained nonlinear optimization. We get the iterative direction by solving quadratic model via affine scaling conjugate gradient and Lanczos methods. By using the line search backtracking technique, we will find an acceptable trial step length along this direction which makes the iterate point strictly feasible and the objective function nonmonotonically decreasing. Global convergence and local superlinear convergence rate of the proposed algorithm are established under some reasonable conditions. Finally, we present some numerical results to illustrate the effectiveness of the proposed algorithm.

• 대한의용생체공학회:의공학회지
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• 제44권1호
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• pp.85-91
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• 2023

Stress urinary incontinence (SUI) occurs when abdominal pressure increases, such as sneezing, exercising, and laughing. Surgical and non-surgical treatments are the common methods of SUI treatment; however, the conventional treatments still require continuous and invasive treatment. Laser have been used to treat SUI, but excessive temperature increase often causes thermal burn on urethra tissue. Therefore, the optimal conditions must be considered to minimize the thermal damage for the laser treatment. The current study investigated the feasibility of the laser irradiation condition for SUI treatment using non-ablative 980 nm laser from a safety perspective through numerical simulations. COMSOL Multiphysics was used to analyze the numerical simulation model. The Pennes bioheat equation with the Beer's law was used to confirm spatio-temporal temperature distributions, and Arrhenius equation defined the thermal damage caused by the laser-induced heat. Ex vivo porcine urethral tissue was tested to validate the extent of both temperature distribution and thermal damage. The temperature distribution was symmetrical and uniformly observed in the urethra tissue. A muscle layer had a higher temperature (28.3 ℃) than mucosal (23.4 ℃) and submucosal layers (25.5 ℃). MT staining revealed no heat-induced collagen and muscle damage. Both control and treated groups showed the equivalent thickness and area of the urethral mucosal layer. Therefore, the proposed numerical simulation can predict the appropriate irradiation condition (20 W for 15 s) for the SUI treatment with minimal temperature-induced tissue.