• 제어로봇시스템학회:학술대회논문집
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• 2000.10a
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• pp.23-23
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• 2000

In this paper, we proposed the problems of robust stability and 개bust H$_{\infty}$ control of discrete time-delay linear st.stems with Frobenius norm-bounded uncertainties. The existence condition and the design method of robust H$_{\infty}$ state feedback control]or are given. Through some changes of variables and Schur complement, the obtained sufficient condition can be rewritten as an LMI(linear matrix inequality) form in terms of all variables.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.12 no.2
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• pp.3-10
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• 2002

For efficient implementation of scalar multiplication in Kobliz elliptic curves, Frobenius endomorphism is useful. Instead of binary expansion of scalar, using Frobenius expansion of scalar we can speed up scalar multiplication and so fast scalar multiplication is closely related to the expansion length of integral multipliers. In this paper we propose a new idea to reduce the length of Frobenius expansion of integral multipliers of scalar multiplication, which makes speed up scalar multiplication. By using the element whose norm is equal to a prime instead of that whose norm is equal to the order of a given elliptic curve we optimize the length of the Frobenius expansion. It can reduce more the length of the Frobenius expansion than that of Solinas, Smart.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.40 no.7
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• pp.1257-1265
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• 2015

In this paper, we describe a greedy user selection scheme for multiuser multiple-input multiple-output (MIMO) systems. We propose a new metric which has significantly improved performance compared to the Frobenius norm metric. The approximation of projection matrix is applied to increase the accuracy of Frobenius norm of effective channel matrix. We analyze the computational complexity of two metrics by using flop counts, and also verify the achievable sum rate through numerical simulation. Our simulation result shows that the proposed metric can achieve the improved sum rate as the number of user antenna increases.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.41 no.8
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• pp.917-920
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• 2016

SpSF algorithm is direction-of-arrival estimation algorithm based on sparse representation of incident signlas. Cost function to be optimized for DOA estimation is multi-dimensional nonlinear function, which is hard to handle for optimization. After some manipulation, the problem can be cast into convex optimiztion problem. Convex optimization problem tuns out to be constrained optimization problem, where the parameter in the constraint has to be determined. The solution of the convex optimization problem is dependent on the specific parameter value in the constraint. In this paper, we propose a rule-of-thumb for determining the parameter value in the constraint. Based on the fact that the noise in the array elements is complex Gaussian distributed with zero mean, the average of the Frobenius norm of the matrix in the constraint can be rigorously derived. The parameter in the constrint is set to be two times the average of the Frobenius norm of the matrix in the constraint. It is shown that the SpSF algorithm actually works with the parameter value set by the method proposed in this paper.

• Proceedings of the KIEE Conference
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• 1992.07a
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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.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.25 no.3
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• pp.107-116
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• 2021

We introduce optimization algorithms using Bregman Divergence for solving non-negative matrix factorization (NMF) problems. Bregman divergence is known a generalization of some divergences such as Frobenius norm and KL divergence and etc. Some algorithms can be applicable to not only NMF with Frobenius norm but also NMF with more general Bregman divergence. Matrix Factorization is a popular non-convex optimization problem, for which alternating minimization schemes are mostly used. We develop the Bregman proximal gradient method applicable for all NMF formulated in any Bregman divergences. In the derivation of NMF algorithm for Bregman divergence, we need to use majorization/minimization(MM) for a proper auxiliary function. We present algorithmic aspects of NMF for Bregman divergence by using MM of auxiliary function.

• Bulletin of the Korean Mathematical Society
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• v.56 no.5
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• pp.1273-1283
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• 2019

In matrix analysis, the Wielandt-Mirsky conjecture states that $$dist({\sigma}(A),{\sigma}(B)){\leq}{\parallel}A-B{\parallel}$$ for any normal matrices $A,B{\in}{\mathbb{C}}^{n{\times}n}$ and any operator norm ${\parallel}{\cdot}{\parallel}$ on $C^{n{\times}n}$. Here dist(${\sigma}(A),{\sigma}(B)$) denotes the optimal matching distance between the spectra of the matrices A and B. It was proved by A. J. Holbrook (1992) that this conjecture is false in general. However it is true for the Frobenius distance and the Frobenius norm (the Hoffman-Wielandt inequality). The main aim of this paper is to study the Hoffman-Wielandt inequality and some weaker versions of the Wielandt-Mirsky conjecture for matrix polynomials.

• The Journal of the Korea institute of electronic communication sciences
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• v.19 no.1
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• pp.31-38
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• 2024

The digital phase-locked loop(DPLL) is one of the circuits composed of a digital detector, digital loop filter, voltage-controlled oscillator, and divider as a fundamental circuit, widely used in many fields such as electrical and circuit fields. A state estimator using various mathematical algorithms is used to improve the performance of a digital phase-locked loop. Traditional state estimators have utilized Kalman filters of infinite impulse response state estimators, and digital phase-locked loops based on infinite impulse response state estimators can cause rapid performance degradation in unexpected situations such as inaccuracies in initial values, model errors, and various disturbances. In this paper, we propose a two-layer Frobenius norm-based finite impulse state estimator to design a new digital phase-locked loop. The proposed state estimator uses the estimated state of the first layer to estimate the state of the first layer with the accumulated measurement value. To verify the robust performance of the new finite impulse response state estimator-based digital phase locked-loop, simulations were performed by comparing it with the infinite impulse response state estimator in situations where noise covariance information was inaccurate.

• Kyungpook Mathematical Journal
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• v.61 no.3
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• pp.583-590
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• 2021

In this work we give new upper and lower bounds for the numerical radius of a complex square matrix A using the entries and the trace of A.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.24 no.9A
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• pp.1322-1328
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• 1999

In this paper, we propose a Multiple Signal Classification(MUSIC) in conjunction with signal enhancement (SE-MUSIC) for solving the direction-of-arrival estimation problem of multiple incoherent plane waves incident on a uniform linear array. The proposed SE-MUSIC algorithms involve the following main two-step procedure : ( i )to find the enhanced matrix that possesses the prescribed properties and which lies closest to a given covariance matrix estimate in the Frobenius norm sense and (ii) to apply the MUSIC to the enhanced matrix. Simulation results are illustrated to demonstrate the better resolution and statistical performance of the proposed method than MUSIC at lower SNR.