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SPLITTING METHOD OF DENSE COLUMNS IN SPARSE LINEAR SYSTEMS AND ITS IMPLEMENTATION
Oh, Seyoung,Kwon, Sun Joo 충청수학회 1997 충청수학회지 Vol.10 No.1
It is important to solve the large sparse linear system appeared in many application field such as $AA^Ty={\beta}$ efficiently. In solving this linear system, the sparse solver using the splitting method for the relatively dense column is experimentally better than the direct solver using the Cholesky method.
ESOR METHOD WITH DIAGONAL PRECONDITIONERS FOR SPD LINEAR SYSTEMS
Oh, Seyoung,Yun, Jae Heon,Kim, Kyoum Sun The Korean Society for Computational and Applied M 2015 Journal of applied mathematics & informatics Vol.33 No.1
In this paper, we propose an extended SOR (ESOR) method with diagonal preconditioners for solving symmetric positive definite linear systems, and then we provide convergence results of the ESOR method. Lastly, we provide numerical experiments to evaluate the performance of the ESOR method with diagonal preconditioners.
Convergence of relaxed two-stage multisplitting method using M-splittings or SOR multisplitting
SeYoung Oh,윤재헌 한국전산응용수학회 2009 Journal of applied mathematics & informatics Vol.27 No.3
In this paper, we study the convergence of relaxed two-stagemultisplitting method using M-splittings or SOR multisplitting as innersplittings and an outer splitting for solving a linear system whose coefficientmatrix is an M-matrix. We also provide numerical experiments for theconvergence of the relaxed two-stage multisplitting method.
Oh, SeYoung,Kwon, SunJoo Chungcheong Mathematical Society 2014 충청수학회지 Vol.27 No.4
In this paper, we present an efficient way to determine a suitable value of the regularization parameter using the global generalized cross validation and analyze the experimental results from preconditioned global conjugate gradient linear least squares(Gl-CGLS) method in solving image deblurring problems. Preconditioned Gl-CGLS solves general linear systems with multiple right-hand sides. It has been shown in [10] that this method can be effectively applied to image deblurring problems. The regularization parameter, chosen from the global generalized cross validation, with preconditioned Gl-CGLS method can give better reconstructions of the true image than other parameters considered in this study.
CHOOSING REGULARIZATION PARAMETER BY GLOBAL L-CURVE CRITERION
Oh, SeYoung,Kwon, SunJoo Chungcheong Mathematical Society 2017 충청수학회지 Vol.30 No.1
As an efficient way to determine the regularization parameter in the discrete ill-posed problems with multiple right-hand sides, we suggest global L-curve criterion as an extension of L-curve technique for image restoration problems with single right-hand side.
THE FAST TRUNCATED LAGRANGE METHOD FOR IMAGE DEBLURRING WITH ANTIREFLECTIVE BOUNDARY CONDITIONS
Oh, SeYoung,Kwon, SunJoo Chungcheong Mathematical Society 2018 충청수학회지 Vol.31 No.1
In this paper, under the assumption of the symmetry point spread function, antireflective boundary conditions(AR-BCs) are considered in connection with the fast truncated Lagrange(FTL) method. The FTL method is proposed as an image restoration method for large-scale ill-conditioned BTTB(block Toeplitz with Toeplitz block) and BTHHTB(block Toeplitz-plus-Hankel matrix with Toeplitz-plus-Hankel blocks) linear systems([13, 17]). The implementation and efficiency of the FTL method in the AR-BCs are further illustrated. Especially, by employing the AR-BCs, both the continuity of the image and the continuity of its normal derivative are preserved at the boundary. A reconstructed image with less artifacts at the boundary is obtained as a result.
A Parallel Algorithm for Large-Scale Linear Programs with a Special Structure
Oh, Seyoung 충청수학회 1993 충청수학회지 Vol.6 No.1
A new sequential algorithm and computational results for large-scale linear programs with a special structure were presented in the previous paper [9]. In this paper, a parallel version of the algorithm was developed for a hypercube multiprocessor architecture NCUBE2. Computational results using 128 processors are presented for a randomly generated large-scale sparse or dense problems with the number of variables up to 256 and constraints up to 5 million.
AN ALGORITHM FOR MULTIPLICATIONS IN F<SUB>2</SUB><SUB>m</SUB>
Oh, SeYoung,Yoon, ChungSup 충청수학회 2003 충청수학회지 Vol.15 No.2
An efficient algorithm for the multiplication in a binary finite filed using a normal basis representation of $F_{2^m}$ is discussed and proposed for software implementation of elliptic curve cryptography. The algorithm is developed by using the storage scheme of sparse matrices.
A Multiple Updating Algorithm for the Leontief Systems
Oh, Seyoung 충남대학교 자연과학연구소 1994 忠南科學硏究誌 Vol.21 No.2
A new algorithm is presented here for the efficient solution of the Leontief models. A structure of particular interest occurs when a industry decides the maximum marginal cost for some products. The present algorithm permits multiple exchanges in the basis at each iteration for the dual problem of the original problem.