• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.22 no.3
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• pp.155-162
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• 2018

We describe a parallel implementation of a relaxed Hermitian and skew-Hermitian splitting preconditioner for the numerical solution of saddle point problems arising from the steady incompressible Navier-Stokes equations. The equations are linearized by the Picard iteration and discretized with the finite element and finite difference schemes on two-dimensional and three-dimensional domains. We report strong scalability results for up to 32 cores.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.22 no.3
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• pp.201-215
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• 2018

In this paper we consider a class of singularly perturbed system of delay differential equations of convection diffusion type with integral boundary conditions. A finite difference scheme on an appropriate piecewise Shishkin type mesh is suggested to solve the problem. We prove that the method is of almost first order convergent. An error estimate is derived in the discrete maximum norm. Numerical experiments support our theoretical results.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.9 no.1
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• pp.31-53
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• 2005

We analyze some real data and, from the background of analysis of data, we define a multi-dimensional jump-type asset model which is derived from short-sampling asset prices. We study some basic properties of this asset model.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.7 no.1
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• pp.47-61
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• 2003

Two principally different statements of the problem of stable numerical differentiation are considered. It is analyzed when it is possible in principle to get a stable approximation to the derivative ${\Large f}'$ given noisy data ${\Large f}_{\delta}$. Computational aspects of the problem are discussed and illustrated by examples. These examples show the practical value of the new understanding of the problem of stable differentiation.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.4 no.2
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• pp.135-142
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• 2000

We consider a multigrid algorithm for higher order finite difference scheme for the Poisson problem on rectangular domain. Several smoothers including Jacobi, Red-black Gauss-Seidel are tested and compared. Since higher order scheme gives much more accurate result then 5-point scheme, one may use small number of levels with higher order scheme and thus the overall cost is reduced quite a lot. The numerical experiment compares the two cases.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.2 no.1
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• pp.88-93
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• 1998

It is frequently important to approximate a rational B$\acute{e}$zier curve by an integral, i.e., polynomial one. This need will arise when a rational B$\acute{e}$zier curve is produced in one CAD system and is to be imported into another system, which can only handle polynomial curves. The objective of this paper is to present an algorithm to approximate rational B$\acute{e}$zier curves with polynomial curves of higher degree.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.4 no.2
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• pp.1-9
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• 2000

An algorithmic approach to degree elevation of B-spline curves is presented. The new algorithms are based on the blossoming process and its matrix representation. The elevation method is introduced that consists of the following steps: (a) decompose the B-spline curve into piecewise $B{\acute{e}}zier$ curves, (b) degree elevate each $B{\acute{e}}zier$ piece, and (c) compose the piecewise $B{\acute{e}}zier$ curves into B-spline curve.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.12 no.1
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• pp.1-6
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• 2008

Duggal-Jeon-Kubrusly([2]) introduced Hilbert space operator T satisfying property ${\mid}T{\mid}^2{\leq}{\mid}T^2{\mid}$, where ${\mid}T{\mid}=(T^*T)^{1/2}$. In this paper we extend this property to general version, namely property B(n). In addition, we construct examples which distinguish the classes of operators with property B(n) for each $n{\in}\mathbb{N}$.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.16 no.2
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• pp.93-105
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• 2012

In this paper, we consider the controllability of a certain class of impulsive neutral evolution differential equations in Banach spaces. Sufficient conditions for controllability are obtained by using the Hausdorff measure of noncompactness and Monch fixed point theorem under the assumption of noncompactness of the evolution system.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.7 no.2
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• pp.51-64
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• 2003

Analysis is given of construction and stability of complex symmetric analogues of Householder matrices, with applications to the eigenproblem for such matrices. We investigate numerical properties of the deflation of complex symmetric matrices by using complex symmetric Householder transformations. The proposed method is very similar to the well-known deflation technique for real symmetric matrices (Cf. [16], pp. 586-595). In this paper we present an error analysis of one step of the deflation of complex symmetric matrices.