• KSII Transactions on Internet and Information Systems (TIIS)
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• v.14 no.6
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• pp.2634-2648
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• 2020

In this paper, an adaptive sparse singular value decomposition (ASSVD) algorithm is proposed to estimate the signal matrix when only one data matrix is observed and there is high dimensional white noise, in which we assume that the signal matrix is low-rank and has sparse singular vectors, i.e. it is a simultaneously low-rank and sparse matrix. It is a structured matrix since the non-zero entries are confined on some small blocks. The proposed algorithm estimates the singular values and vectors separable by exploring the structure of singular vectors, in which the recent developments in Random Matrix Theory known as anisotropic Marchenko-Pastur law are used. And then we prove that when the signal is strong in the sense that the signal to noise ratio is above some threshold, our estimator is consistent and outperforms over many state-of-the-art algorithms. Moreover, our estimator is adaptive to the data set and does not require the variance of the noise to be known or estimated. Numerical simulations indicate that ASSVD still works well when the signal matrix is not very sparse.

• Proceedings of the Korean Society of Broadcast Engineers Conference
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• 2010.07a
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• pp.61-63
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• 2010

Recent work in compressed sensing theory shows that m${\times}$n independent and identically distributed sensing matrices whose entries are drawn independently from certain probability distributions guarantee exact recovery of a sparse signal with high probability even if m${\ll}$n. In particular, it is well understood that the L1 minimization algorithm is able to recover sparse signals from incomplete measurements. In this paper, we propose a novel sparse signal reconstruction method that is based on the reweighted L1 minimization via support recovery.

• Proceedings of the KIEE Conference
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• 2007.04a
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• pp.281-282
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• 2007

We address a new representation of DCT/DFT/Wavelet matrices via one hybrid architecture. Based on an element inverse matrix factorization algorithm, we show that the OCT, OFT and Wavelet which based on Haar matrix have the similarrecursive computational pattern, all of them can be decomposed to one orthogonal character matrix and a special sparse matrix. The special sparse matrix belongs to Jacket matrix, whose inverse can be from element-wise inverse or block-wise inverse. Based on this trait, we can develop a hybrid architecture.

• Journal of the Korean Society for Precision Engineering
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• v.12 no.7
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• pp.99-106
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• 1995

Frequency response functions are of great use in dynamic analysis of structural systems. The present paper proposes an efficient method for computation of the frequency rewponse functions of linear structural dynamic models with a sparse, non-proportional damping matrix. An exact condensation procedure is proposed which enables the present method to condense the matrices without resulting in any errors. Also, an iterative scheme is proposed to be able to avoid matrix inversion in computing frequency response matrix. The proposed method is illustrated through a numerical example.

• Journal of the Chungcheong Mathematical Society
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• v.15 no.2
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• pp.97-107
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• 2003

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.

• Journal of Advanced Navigation Technology
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• v.13 no.1
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• pp.62-67
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• 2009

The demand for high performance computer grows to solve large linear systems of equations in such engineering fields - circuit simulation for VLSI design, image processing, structural engineering, aerodynamics, etc. Many various parallel processing systems have been proposed and manufactured to satisfy the demand. The properties of linear system determine what algorithm is proper to solve the problem. Direct methods or iterative methods can be used for solving the problem. In this paper, an intelligent parallel iterative method for solving linear systems of equations with large sparse matrices is proposed and its efficiency is proved through simulation.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.11 no.4
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• pp.143-150
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• 1991

This paper presents an overview of a system of computer programs for the solution of a large geodetic network of about 2,000 stations. The system arranges the matrices in systematic sparse form which is applied to observation equations of RR(C)U (Row-wise Representation Complete Unordered) type and to normal equations of RR(U)U (Row-wise Representation Upper Unordered) type. The solution is done by a Modified Cholesky's algorithm in view of large networks. The implementation program are tested in PC-386 by korean new secondary networks, the results show that the sparse techniques are highly useful to geodetic networks in core-storage management and processing time.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.5 no.1
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• pp.85-100
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• 2001

In this paper we propose a block-type parallel preconditioner for solving large sparse nonsymmetric linear systems, which we expect to be scalable. It is Multi-Color Block SOR preconditioner, combined with direct sparse matrix solver. For the Laplacian matrix the SOR method is known to have a nondeteriorating rate of convergence when used with Multi-Color ordering. Since most of the time is spent on the diagonal inversion, which is done on each processor, we expect it to be a good scalable preconditioner. Finally, due to the blocking effect, it will be effective for ill-conditioned problems. We compared it with four other preconditioners, which are ILU(0)-wavefront ordering, ILU(0)-Multi-Color ordering, SPAI(SParse Approximate Inverse), and SSOR preconditioner. Experiments were conducted for the Finite Difference discretizations of two problems with various meshsizes varying up to 1024 x 1024, and for an ill-conditioned matrix from the shell problem from the Harwell-Boeing collection. CRAY-T3E with 128 nodes was used. MPI library was used for interprocess communications. The results show that Multi-Color Block SOR and ILU(0) with Multi-Color ordering give the best performances for the finite difference matrices and for the shell problem only the Multi-Color Block SOR converges.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.34 no.1
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• pp.1-9
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• 2024

Multivariate Quadratic (MQ)-based digital signature schemes have advantages such as ease of implementation and small signature sizes, making them promising candidates for post-quantum cryptography. To enhance the efficiency of such MQ-based digital signature schemes, utilizing sparse matrices have been proposed, including HiMQ, which has been standardized by Korean Telecommunications Technology Association standard. However, HiMQ shares a similar key structure with Rainbow, which is a representative MQ-based digital signature scheme and was broken by the MinRank attack proposed in 2022. While HiMQ was standardized by a TTA and recommended parameters were provided, these parameters were based on cryptanalysis as of 2020, without considering recent attacks. In this paper, we examine attacks applicable to MQ-based digital signatures, specifically targeting HiMQ, and perform a security analysis. The most effective attack against HiMQ is the combined attack, an improved version of the MinRank attack proposed in 2022, and none of the three recommended parameters satisfy the desired security strength. Furthermore, HiMQ-128 and HiMQ-160 do not meet the minimum security strength requirement of 128-bit security level.

• Journal of the Institute of Electronics Engineers of Korea TC
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• v.45 no.2
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• pp.1-5
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• 2008

Although we can make a sparse matrices for LDPC codes, the encoding complexity per a block increases quadratically by $n^2$. We propose modified PEG algorithm using PEG algorithm having a large girth by establishing edges or connections between symbol and check nodes in an edge-by-edge manner. M-PEG construct parity check matrices. So we propose parity check matrices H form a dual-diagonal matrices that can construct a more efficient decoder using a M-PEG(modified Progressive Edge Growth).