• Communications of the Korean Mathematical Society
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• v.9 no.3
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• pp.753-765
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• 1994

The linearly constrained quadratic programming(QP) considered is : $$ min f(x) = c^T x + \frac{1}{2}x^T Hx $$ $$ (1) subject to A^T x \geq b,$$ where $c,x \in R^n, b \in R^m, H \in R^{n \times n)}$, symmetric, and $A \in R^{n \times n}$. If there are bounds on x, these are included in the matrix $A^T$. The Hessian matrix H may be positive definite or negative semi-difinite. For large problems H and the constraint matrix A are assumed to be sparse.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.46 no.5
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• pp.25-31
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• 2009

The recently developed sampling theory, "compressed sensing" is gathering huge interest in MR reconstruction area because of its feasibility of high spatio-temporal resolution of dynamic MRI which has been limited in conventional methods based on Nyquist sampling theory. Since dynamic MRI usually has high redundant information along temporal direction, this can be very sparsely represented in most of cases. Therefore, compressed sensing that exploits the sparsity of unknown images can be effectively applied in most of dynamic MRI. This review article briefly introduces currently proposed compressed sensing based dynamic MR imaging algorithms and other methods exploiting sparsity. By comparing them with conventional methods, you may have insight how the compressed sensing based methods can impact nearly every area of clinical dynamic MRI.

• The Journal of the Acoustical Society of Korea
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• v.35 no.5
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• pp.383-388
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• 2016

We develop two methods to select a constant in the RLS (Recursive Least Squares) with the convex regularization. The RLS with the convex regularization was proposed by Eksioglu and Tanc in order to estimate the sparse acoustic channel. However the algorithm uses the regularization constant which needs the information about the true channel response for the best performance. In this paper, we propose two methods to select the regularization constant which don't need the information about the true channel response. We show that the estimation performance using the proposed methods is comparable with the Eksioglu and Tanc's algorithm.

• Journal of the Korea Society of Computer and Information
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• v.17 no.9
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• pp.9-16
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• 2012

In this paper, we propose the two dimensional variable-length vector storage format which can be used for efficient storage of sparse matrix in the FEM (finite element method). The proposed storage format is the method storing only actual needed non-zero values of each row on upper triangular matrix with the total rows N, by using two dimensional variable-length vector instead of $N{\times}N$ large sparse matrix of entire equation of finite elements. This method only needs storage spaces of the number of minimum 1 to maximum 5 in 2D grid structure and the number of minimum 1 to maximum 14 in 3D grid structure of analysis target. The number doesn't excess two times although involving index number. From the experimental result, we can find out that the proposed storage format can reduce the memory space more effectively, as the total number of nodes increases, than the existing skyline storage format storing maximum column height.

• Journal of applied mathematics & informatics
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• v.26 no.1_2
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• pp.213-222
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• 2008

Iterative methods are often suitable for solving least squares problems min$||Ax-b||_2$, where A $\epsilon\;\mathbb{R}^{m{\times}n}$ is large and sparse. The well known LSQR algorithm is among the iterative methods for solving these problems. A good preconditioner is often needed to speedup the LSQR convergence. In this paper we present the numerical experiments of applying a well known preconditioner for the LSQR algorithm. The preconditioner is based on the $A^T$ A-orthogonalization process which furnishes an incomplete upper-lower factorization of the inverse of the normal matrix $A^T$ A. The main advantage of this preconditioner is that we apply only one of the factors as a right preconditioner for the LSQR algorithm applied to the least squares problem min$||Ax-b||_2$. The preconditioner needs only the sparse matrix-vector product operations and significantly reduces the solution time compared to the unpreconditioned iteration. Finally, some numerical experiments on test matrices from Harwell-Boeing collection are presented to show the robustness and efficiency of this preconditioner.

• Journal of Broadcast Engineering
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• v.10 no.2
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• pp.166-173
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• 2005

In this paper, we propose a mobile channel estimation algorithm using matching pursuit algorithm for orthogonal frequency division multiplexing (OFDM) systems. Least square (LS) algorithm, which is used as a conventional channel estimation algorithm for OFDM systems, has error probability of channel estimation affected by effects of noise. By estimating the channel of sparse type, the proposed algorithm reduces effects of noise during time intervals that multi-path signal doesn't exist. The proposed algorithm estimates a mobile receivingchannel using pilot information transmitted consequently. We compare performance of the proposed algorithm with the LS algorithm by measuring symbol error rate with 64QAM under a mobile multi-path fading channel model.

• Communications for Statistical Applications and Methods
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• v.5 no.3
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• pp.707-722
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• 1998

This paper evaluates a new clinical trial designs for low infection rate disease. This type of sparse disease reaction makes the traditional two sample t-test or Wilcoxon rank-sum test inefficient compared to a new test suggested. The new test, which is based solely on the larger changes, is shown to be more effective than existing method by simulation for small samples. However, this test can be shown to be connected to the locally most powerful rank test under certain practical conditions. This design is motivated in testing the treatment effects in periodontal disease research.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.5 no.2
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• pp.63-69
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• 2001

In this study, we shall be concerned with computing in parallel a few of the smallest eigenvalues and their corresponding eigenvectors of the eigenvalue problem, $Ax={\lambda}Bx$, where A is symmetric, and B is symmetric positive definite. Both A and B are large and sparse. Recently iterative algorithms based on the optimization of the Rayleigh quotient have been developed, and CG scheme for the optimization of the Rayleigh quotient has been proven a very attractive and promising technique for large sparse eigenproblems for small extreme eigenvalues. As in the case of a system of linear equations, successful application of the CG scheme to eigenproblems depends also upon the preconditioning techniques. A proper choice of the preconditioner significantly improves the convergence of the CG scheme. The idea underlying the present work is a parallel computation of the Multi-Color Block SSOR preconditioning for the CG optimization of the Rayleigh quotient together with deflation techniques. Multi-Coloring is a simple technique to obatin the parallelism of order n, where n is the dimension of the matrix. Block SSOR is a symmetric preconditioner which is expected to minimize the interprocessor communication due to the blocking. We implemented the results on the CRAY-T3E with 128 nodes. The MPI(Message Passing Interface) library was adopted for the interprocessor communications. The test problems were drawn from the discretizations of partial differential equations by finite difference methods.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.39A no.7
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• pp.424-430
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• 2014

In this paper, we propose a compressed sensing-based signal recovery technique for an uplink multi-user spatial modulation (MU-SM) system. In the MU-SM system, only one antenna among $N_t$ antennas of each user becomes active by nature. Thus, this characteristics is exploited for signal recovery at a base station. We modify the conventional orthogonal matching pursuit (OMP) algorithm which has been widely used for sparse signal recovery in literature for the MU-SM system, which is called MU-OMP. We also propose a parallel OMP algorithm for the MU-SM system, which is called MU-POMP. Specifically, in the proposed algorithms, antenna indices of a specific user who was selected in the previous iteration are excluded in the next iteration of the OMP algorithm. Simulation results show that the proposed algorithms outperform the conventional OMP algorithm in the MU-SM system.

• Proceedings of the Korean Statistical Society Conference
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• 2002.05a
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• pp.29-34
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• 2002

$p=(p_{}1,p_{2},{\cdots},p_{k})^{T}$의 확률벡터를 가진 다항분포로부터 관측된 칸 돗수(cell frequency) 벡터가 $N=(N_{1},N_{2},{\cdots},N_{k})^{T}$이며 ${\sum}{\limits}_{j=1}^{k}N_{j}=n$이라 하자. 총돗수 n이 칸의 총갯수 k에 비하여 상대적으로 매우 작을 때 이러한 이산형 자료를 희박다항분포자료(sparse multinomial data)라 한다. 이러한 희박다항분포자료의 칸들이 순서화 되어 있을 때 우리는 i번째 칸의 확률 $p_{i}$를 돗수 추정량 $N_{j}/n$ 들을 평활함으로써 추정 할 수 있다. Aerts, et al.(1997)과 Baek(1998) 등에 의해 제안된 국소최소제곱기준에 근거한 국소다항커널추정량은 희박점근일치성의 좋은 성질을 가짐에도 불구하고 확률추정지가 음수값을 가질 수 있는 단점을 내포하고 있다. 본 연구에서는 이러한 단점을 극복하기 위하여 국소최대우도 기준에 근거한 새로운 커널추정량을 제안하고, 그것의 점근적 성질을 연구하였다.