• Proceedings of the KIEE Conference
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• 대한전기학회 1992년도 하계학술대회 논문집 A
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• pp.296-298
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• 1992

Presented in this paper is a generalized norm bound for the continuous and discrete algebraic Riccati equations. The generalized norm bound provides a lower bound of the Riccati solutions specified by any kind of submultiplicative matrix norms including the spectral, Frobenius and $\ell_1$ norms.

• Korean Journal of Mathematics
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• 제22권1호
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• pp.123-131
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• 2014

The purpose of this paper is to study the perturbation analysis of the matrix equation $X=I-A^*X^{-1}A+B^*X^{-1}B$. Based on the matrix differentiation, we give a precise perturbation bound for the positive definite solution. A numerical example is presented to illustrate the shrpness of the perturbation bound.

• Communications for Statistical Applications and Methods
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• 제12권3호
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• pp.653-657
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• 2005

Eigenstructure of a spatial design matrix of Matheron's variogram estimator in $R^1$ is derived. It is shown that the spatial design matrix in $R^1$ with n/2$\le$h < n has a nice spectral decomposition. The mean, variance, and covariance of this estimator are obtained using the eigenvalues of a spatial design matrix. We also found that the lower bound and the upper bound of the normalized Matheron's variogram estimator.

• Transactions on Control, Automation and Systems Engineering
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• 제1권1호
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• pp.44-49
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• 1999

This paper presents a new T-S(Tae-Sugeno) fuzzy controller design method satisfying the output energy bound. Maximum output energy via a quadratic Lyapunov function to obtain the bound on output energy is derived. LMI(Linear Matrix Inequality) problems which satisfy an output energy bound for both of the continuous-time and discrete-time T-S fuzzy control system are also derived. Solving these LMIs simultaneously, we find a common symmetric positive definite matrix P which guarantees the global asymptotic stability of the system and stable feedback gains K's satisfying the output energy bound. A simple example demonstrates validity of the proposed design method.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제20권2호
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• pp.107-121
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• 2016

We analyze the complexity of the LLL algorithm, invented by Lenstra, Lenstra, and $Lov{\acute{a}}sz$ as a a well-known lattice reduction (LR) algorithm which is previously known as having the complexity of $O(N^4{\log}B)$ multiplications (or, $O(N^5({\log}B)^2)$ bit operations) for a lattice basis matrix $H({\in}{\mathbb{R}}^{M{\times}N})$ where B is the maximum value among the squared norm of columns of H. This implies that the complexity of the lattice reduction algorithm depends only on the matrix size and the lattice basis norm. However, the matrix structures (i.e., the correlation among the columns) of a given lattice matrix, which is usually measured by its condition number or determinant, can affect the computational complexity of the LR algorithm. In this paper, to see how the matrix structures can affect the LLL algorithm's complexity, we derive a more tight upper bound on the complexity of LLL algorithm in terms of the condition number and determinant of a given lattice matrix. We also analyze the complexities of the LLL updating/downdating schemes using the proposed upper bound.

• International Journal of Control, Automation, and Systems
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• 제6권5호
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• pp.776-784
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• 2008

In this paper, new upper matrix bounds for the solution of the continuous algebraic Riccati equation (CARE) are derived. Following the derivation of each bound, iterative algorithms are developed for obtaining sharper solution estimates. These bounds improve the restriction of the results proposed in a previous paper, and are more general. The proposed bounds are always calculated if the stabilizing solution of the CARE exists. Finally, numerical examples are given to demonstrate the effectiveness of the present schemes.

• Journal of applied mathematics & informatics
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• 제25권1_2호
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• pp.169-181
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• 2007

Applying the properties of Hadamard core for totally nonnegative matrices, we give new lower bounds of the determinant for Hadamard product about matrices in Hadamard core and totally nonnegative matrices, the results improve Oppenheim inequality for tridiagonal oscillating matrices obtained by T. L. Markham.

• Journal of Ginseng Research
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• 제18권1호
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• pp.10-16
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• 1994

Effects of ginsenosides on the activities of bovine liver mitochondrial matrix ALDH and membrane bound ALDH were observed in vitro and it was found that both matrix and membrane bound ALDH were stimulated appreciably. The maximum activity for the matrix AkDH was found at the concentration of ginsenoside mixture being $10^{-7}$~$10^5$% and that for the membrane bound ALDH was at $10^{-6}$~$10^{-4}$%. It was also found that Km values of both ALDHS were lowered and their maximum velocity was increased. It was realized that the bovine liver mitochondrial matrix AkDH is Quite specific for the oxidation of low aliphatic aldehydes such as acetaldehyde and propionaldehyde. Therefore the increase of Vmax/Km value of the matrix ALDH in the presence of ginsenosides suggest that ginsenosides might stimulate the ALDH activity thereby resulting in the quick removal of harmful acetaldehyde from the liver to protect its toxicity.

• Journal of Communications and Networks
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• 제10권1호
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• pp.5-9
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• 2008

Researchers have investigated many upper bound techniques applicable to error probabilities on the maximum likelihood (ML) decoding performance of turbo-like codes and low density parity check (LDPC) codes in recent years for a long codeword block size. This is because it is trivial for a short codeword block size. Previous research efforts, such as the simple bound technique [20] recently proposed, developed upper bounds for LDPC codes and turbo-like codes using ensemble codes or the uniformly interleaved assumption. This assumption bounds the performance averaged over all ensemble codes or all interleavers. Another previous research effort [21] obtained the upper bound of turbo-like code with a particular interleaver using a truncated union bound which requires information of the minimum Hamming distance and the number of codewords with the minimum Hamming distance. However, it gives the reliable bound only in the region of the error floor where the minimum Hamming distance is dominant, i.e., in the region of high signal-to-noise ratios. Therefore, currently an upper bound on ML decoding performance for turbo-like code with a particular interleaver and LDPC code with a particular parity check matrix cannot be calculated because of heavy complexity so that only average bounds for ensemble codes can be obtained using a uniform interleaver assumption. In this paper, we propose a new bound technique on ML decoding performance for turbo-like code with a particular interleaver and LDPC code with a particular parity check matrix using ML estimated weight distributions and we also show that the practical iterative decoding performance is approximately suboptimal in ML sense because the simulation performance of iterative decoding is worse than the proposed upper bound and no wonder, even worse than ML decoding performance. In order to show this point, we compare the simulation results with the proposed upper bound and previous bounds. The proposed bound technique is based on the simple bound with an approximate weight distribution including several exact smallest distance terms, not with the ensemble distribution or the uniform interleaver assumption. This technique also shows a tighter upper bound than any other previous bound techniques for turbo-like code with a particular interleaver and LDPC code with a particular parity check matrix.

• The Journal of Korean Institute of Communications and Information Sciences
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• 제29권10C호
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• pp.1363-1369
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• 2004

LDPC(Low Density Parity Check) codes are described by bipartite graphs with bit nodes and parity-check nodes. Tanner derived minimum distance bounds of the regular LDPC code in terms of the eigenvalues of the associated adjacency matrix. In this paper we generalize the Tanner's results. We derive minimum distance bounds applicable to both regular and blockwise-irregular LDPC codes. The first bound considers the relation between bit nodes in a minimum-weight codeword, and the second one considers the connectivity between parity nodes adjacent to a minimum-weight codeword. The derived bounds make it possible to describe the distance property of the code in terms of the eigenvalues of the associated matrix.