• Journal of applied mathematics & informatics
• /
• v.38 no.3_4
• /
• pp.261-269
• /
• 2020

For any Banach spaces X and Y, let L(X, Y) denote the set of all bounded linear operators from X to Y. Let A ∈ L(X, Y) and B, C ∈ L(Y, X) satisfying operator equation ABA = ACA. In this paper, we prove that AC and BA share the local spectral properties such as a finite ascent, a finite descent, property (K), localizable spectrum and invariant subspace.

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.2 no.1
• /
• pp.1-9
• /
• 1978

냉각용 Fin의 설계문제를 일반적인 최적설계문제로 바꾸어서 일반화된 Steepest Descent 방법에 의한 수치적 방법을 도입하여 해결하였다. 보다 실제적인 문제를 다룰 수 있도록 여러가지 제한조건을 고려한 Fin의 최적곡선 모양의 해를 얻었으며 이 방법의 유용성을 보였다. 사다리꼴의 Fin 설계예에서 위 방법을 이용한 해와 직접 계산에 의한 열전달량의 등고선 그림으로부터 구한 해와 일치함을 보였다.

• 제어로봇시스템학회:학술대회논문집
• /
• 2000.10a
• /
• pp.373-373
• /
• 2000

In this paper, we propose a fuzzy modeling algorithm which divides the input space more efficiently than convention methods by taking into consideration correlations between components of sample data. The proposed fuzzy modeling algorithm consists of two steps: coarse tuning, which determines consequent parameters approximately using FCRM clustering method, and fine tuning, which adjusts the premise and consequent parameters more precisely by gradient descent algorithm. To evaluate the performance of the proposed fuzzy mode, we use the numerical data of nonlinear function.

• Proceedings of the Korean Information Science Society Conference
• /
• 2002.10d
• /
• pp.625-627
• /
• 2002

본 논문에서는 의료영상 인식 기술 중 인식률이 뛰어나고 신뢰성 있는 대뇌출혈성 병변인식 시스템을 구현하기 위하여 신호처리 분야에서 주로 사용되는 Wavelet 변환과 신경망 기법을 이용하고자 한다. 그러나 신경망 기법에서 주로 사용되는 비선형 최적화기법인 Gradient descent BP는 최적화 문제점을 해결하기에는 수렴속도가 느리기 때문에 적합하지 않다. 따라서 본 논문에서는 기존 Gradient descent BP를 보완한 Levenberg-Marquardt Back-Propagation을 대뇌출혈성 병변인식에 적용하여 구현함으로써 총 50개의 패턴 중 45개의 영상이 인식에 성공하였고 전체 평균 인식률은 각각 90%와 87%의 인식률을 보였다.

• Journal of applied mathematics & informatics
• /
• v.11 no.1_2
• /
• pp.201-213
• /
• 2003

In this paper we present a second order PVT (parallel variable transformation) algorithm converging to second order stationary points for minimizing smooth functions, based on the first order PVT algorithm due to Fukushima (1998). The corresponding stopping criterion, descent condition and descent step for the second order PVT algorithm are given.

• Communications of the Korean Mathematical Society
• /
• v.34 no.3
• /
• pp.1029-1047
• /
• 2019

We are interested in the problem of determining the best fitted circle to a set of data points in space. This can be usually obtained by minimizing the geometric distances or various approximate algebraic distances from the fitted circle to the given data points. In this paper, we propose an algorithm in such a way that the sum of the squares of the geometric distances is minimized in ${\mathbb{R}}^3$. Our algorithm is mainly based on the steepest descent method with a view of ensuring the convergence of the corresponding objective function Q(u) to a local minimum. Numerical examples are given.

• Communications of the Korean Mathematical Society
• /
• v.37 no.1
• /
• pp.195-205
• /
• 2022

In this paper, we provide various characterizations for the composition operator on Lorentz spaces L(p, q), 1 < p ≤ ∞, 1 ≤ q ≤ ∞ to have finite ascent (descent) in terms of its inducing measurable transformation. At the end, in order to demonstrate our outcomes, some examples are given.

• Korean Journal of Mathematics
• /
• v.30 no.3
• /
• pp.555-560
• /
• 2022

Suppose L/K be a finite abelian extension of number fields of odd degree and suppose an abelian variety A defined over L is a K-variety. If the endomorphism algebra of A/L is a field F, the followings are equivalent : (1) The enodomorphiam algebra of the restriction of scalars from L to K is simple. (2) There is no proper subfield of L containing L^G_F on which A has a K-variety descent.

• Journal of the Korean Data and Information Science Society
• /
• v.27 no.2
• /
• pp.381-394
• /
• 2016

Graphical model represents conditional dependencies between variables as a graph with nodes and edges. It is widely used in various fields including physics, economics, and biology to describe complex association. Conditional dependencies can be estimated from a inverse covariance matrix, where zero off-diagonal elements denote conditional independence of corresponding variables. This paper proposes a efficient BCDR (block coordinate descent with random permutation) algorithm using graphics processing units and random permutation for the CONCORD (convex correlation selection method) based on the BCD (block coordinate descent) algorithm, which estimates a inverse covariance matrix based on pseudo-likelihood. We conduct numerical studies for two network structures to demonstrate the efficiency of the proposed algorithm for the CONCORD in terms of computation times.

• Journal of the Korea Computer Industry Society
• /
• v.4 no.10
• /
• pp.731-740
• /
• 2003

Since motion estimation remove the redundant data to employ the temporal correlations between adjacent frames in a video sequence, it plays an important role in digital video coding. And in the block matching algorithm, search patterns of different shapes or sizes and the distribution of motion vectors have a large impact on both the searching speed and the image quality. In this paper, we propose a new fast block matching algorithm using the small-cross search pattern and the block-based gradient descent search pattern. Our algorithm first finds the motion vectors that are close to the center of search window using the small-cross search pattern, and then quickly finds the other motion vectors that are not close to the center of search window using the block-based gradient descent search pattern. Through experiments, compared with the block-based gradient descent search algorithm(BBGDS), the proposed search algorithm improves as high as 26-40% in terms of average number of search point per motion vector estimation.