• Kyungpook Mathematical Journal
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• 제59권3호
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• pp.445-464
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• 2019

In this paper, we propose a new iterative algorithm generated by a finite family of accretive operators in a q-uniformly smooth Banach space. We prove the strong convergence of the proposed iterative algorithm. The results presented in this paper are interesting extensions and improvements of known results of Qin et al. [Fixed Point Theory Appl. 2014(2014): 166], Kim and Xu [Nonlinear Anal. 61(2005), 51-60] and Benavides et al. [Math. Nachr. 248(2003), 62-71].

• Journal of applied mathematics & informatics
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• 제28권3_4호
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• pp.939-944
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• 2010

Let H be a real Hilbert space. Let T : $H\;{\rightarrow}\;H$ be an averaged mapping with $F(T)\;{\neq}\;{\emptyset}$. Let {$\alpha_n$} be a real numbers in (0, 1). For given $x_0\;{\in}\;H$, let the sequence {$x_n$} be generated iteratively by $x_{n+1}\;=\;(1\;-\;{\alpha}_n)Tx_n$, $n\;{\geq}\;0$. Assume that the following control conditions hold: (i) $lim_{n{\rightarrow}{\infty}}\;{\alpha}_n\;=\;0$; (ii) $\sum^{\infty}_{n=0}\;{\alpha}_n\;=\;{\infty}$. Then {$x_n$} converges strongly to a fixed point of T.

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제5권2호
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• pp.131-135
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• 2005

This paper proposes an efficient face recognition using independent component analysis(ICA) derived from the fixed point(FP) algorithm based on secant method. The secant method can exclude the complex computation of differential process from the FP based on Newton method. The proposed ICA has been applied to recognize the 20 Yale face images of $324\times324$ pixels. The experimental results show that the proposed ICA is superior to PCA not only in the restoration performance of basis images but also in the recognition performance of the trained images and the test images. Then negative angle as similarity measures has better recognition ratio than city-block and Euclidean.

• Nonlinear Functional Analysis and Applications
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• 제26권5호
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• pp.995-1009
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• 2021

Many iterative algorithms like that Picard, Mann, Ishikawa and S-iteration are very useful to elucidate the fixed point problems of a nonlinear operators in various topological spaces. The recent trend for elucidate the fixed point via inertial iterative algorithm, in which next iterative depends on more than one previous terms. The purpose of the paper is to establish convergence theorems of new inertial Picard normal S-iteration algorithm for nonexpansive mapping in Hilbert spaces. The comparison of convergence of InerNSP and InerPNSP is done with InerSP (introduced by Phon-on et al. [25]) and MSP (introduced by Suparatulatorn et al. [27]) via numerical example.

• Nonlinear Functional Analysis and Applications
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• 제27권3호
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• pp.449-469
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• 2022

This paper deals with the new iterative algorithm for approximating the fixed point of generalized 𝛼-nonexpansive mappings in a hyperbolic space. We show that the proposed iterative algorithm is faster than all of Picard, Mann, Ishikawa, Noor, Agarwal, Abbas, Thakur and Piri iteration processes for contractive mappings in a Banach space. We also establish some weak and strong convergence theorems for generalized 𝛼-nonexpansive mappings in hyperbolic space. The examples and numerical results are provided in this paper for supporting our main results.

• Nonlinear Functional Analysis and Applications
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• 제28권1호
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• pp.175-203
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• 2023

In this paper, we study an iterative algorithm that is based on inertial proximal and contraction methods embellished with relaxation technique, for finding common solution of monotone variational inclusion, and fixed point problems of pseudocontractive mapping in real Hilbert spaces. We establish a strong convergence result of the proposed iterative method based on prediction stepsize conditions, and under some standard assumptions on the algorithm parameters. Finally, some special cases of general problem are given as applications. Our results improve and generalized some well-known and related results in literature.

• 한국정보통신학회논문지
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• 제11권1호
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• pp.46-55
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• 2007

다음은 부동소수점 역수 및 역제곱근 계산에 많이 사용하는 뉴톤-랍손 알고리즘은 일정한 횟수의 곱셈을 반복하여 계산한다. 본 논문에서는 뉴톤-랍손 알고리즘의 반복 과정의 오차를 예측하여 오차가 정해진 값보다 작아지는 시점까지 반복 연산하는 개선된 뉴톤-랍손 알고리즘을 제안한다. 본 논문에서 제안한 알고리즘은 입력 값에 따라서 곱셈 횟수가 다르므로, 평균 곱셈 횟수를 계산하는 방식을 유도하고, 여러 크기의 근사 테이블에서 단정도실수 및 배정도실수의 역수 및 역제곱근 계산에 필요한 평균 곱셈 횟수를 산출한다. 이들 평균 곱셈 횟수를 종래 알고리즘과 비교하여 본 논문에서 제안한 알고리즘의 우수성을 증명한다. 본 논문에서 제안한 알고리즘은 오차가 일정한 값보다 작아질 때까지만 반복 연산을 수행하므로 역수 및 역제곱근 계산기의 성능을 높일 수 있고 최적의 근사 테이블을 구성할 수 있다. 본 논문의 연구 결과는 디지털 신호처리, 컴퓨터 그라픽스, 멀티미디어, 과학 기술 연산 등 부동소수점 계산기가 사용되는 분야에서 폭 넓게 사용될 수 있다.

• 로봇학회논문지
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• 제6권4호
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• pp.308-316
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• 2011

This work deals with development of effective redundancy resolution algorithms for the motion control of manipulator. Differently from the typical kinematically redundant robots that are attached to the fixed ground, the ZMP condition should be taken into account in the manipulator motion in order to guarantee the system stability. In this paper, a new motion planning algorithm for redundant manipulator not fixed to the ground is introduced. A sequential redundancy resolution algorithm is proposed, which ensures the ZMP (Zero Moment Point) stability, the planned operational motion, and additional sub-criteria such as joint limit index. A geometric constraint equation derived by reshaping the existing ZMP equation enables one to employ the sequential redundancy algorithm. The feasibility of the proposed algorithm is verified by simulating a redundant manipulator model.

• 한국통신학회논문지
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• 제30권4C호
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• pp.191-199
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• 2005

최근 무선 이동통신에서 상대적으로 늘어난 다중 접속자들에 대해 대역폭을 효율적으로 사용하면서도 보다 빠른 데이터 전송률을 지원하기 위해 제안된 시공간 turbo 부호에 대한 연구가 많이 이루어지고 있다. 본 논문에서는 시공간 turbo 부호의 복호 시 요구되는 계산량을 줄이기 위해 사전 정보를 근사화하여 이 정보를 고정 소수점 연산 시 간단하게 구현할 수 있는 복호 알고리즘을 제안하였다. 또한 시공간 turbo 부호의 복호 알고리즘을 고정 소수점 연산을 이용하여 구현하였을 때 성능을 해석하였고 Log-MAP 알고리즘의 성능에 근사하는 효율적인 고정 소수점 구현 방법을 제안하였다. 이 방법을 Log-MAP 알고리즘에 적용하여 성능을 분석하였고 기존의 Log-MAP의 결과에 거의 근접한 성능을 보임을 확인하였다.

• 센서학회지
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• 제29권5호
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• pp.348-353
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• 2020

This paper presents an adaptive method to avoid obstacles in various environmental settings, using a two-dimensional (2D) LiDAR sensor for mobile robots. While the conventional reaction based smooth nearness diagram (SND) algorithms use a fixed safety distance criterion, the proposed algorithm autonomously changes the safety criterion considering the obstacle density around a robot. The fixed safety criterion for the whole SND obstacle avoidance process can induce inefficient motion controls in terms of the travel distance and action smoothness. We applied a multinomial logistic regression algorithm, softmax regression, to classify 2D LiDAR point clouds into seven obstacle structure classes. The trained model was used to recognize a current obstacle density situation using newly obtained 2D LiDAR data. Through the classification, the robot adaptively modifies the safety distance criterion according to the change in its environment. We experimentally verified that the motion controls generated by the proposed adaptive algorithm were smoother and more efficient compared to those of the conventional SND algorithms.