• Nonlinear Functional Analysis and Applications
• /
• v.28 no.3
• /
• pp.623-646
• /
• 2023

In this article, we introduce the hyperbolic space version of a faster iterative algorithm. The proposed iterative algorithm is used to approximate the common fixed point of three multi-valued almost contraction mappings and three multi-valued mappings satisfying condition (E) in hyperbolic spaces. The concepts weak w²-stability involving three multi-valued almost contraction mappings are considered. Several strong and △-convergence theorems of the suggested algorithm are proved in hyperbolic spaces. We provide an example to compare the performance of the proposed method with some well-known methods in the literature.

• Journal of the Institute of Electronics Engineers of Korea SD
• /
• v.45 no.6
• /
• pp.49-59
• /
• 2008

SIFT(Scale Invariant Feature Transform) is an algorithm to extract vectors at pixels around keypoints, in which the pixel colors are very different from neighbors, such as vortices and edges of an object. The SIFT algorithm is being actively researched for various image processing applications including 3-D image constructions, and its most computation-intensive stage is a keypoint localization. In this paper, we develope a fixed-point model of the keypoint localization and propose its efficient hardware architecture for embedded applications. The bit-length of key variables are determined based on two performance measures: localization accuracy and error rate. Comparing with the original algorithm (implemented in Matlab), the accuracy and error rate of the proposed fixed point model are 93.57% and 2.72% respectively. In addition, we found that most of missing keypoints appeared at the edges of an object which are not very important in the case of keypoints matching. We estimate that the hardware implementation will give processing speed of $10{\sim}15\;frame/sec$, while its fixed point implementation on Pentium Core2Duo (2.13 GHz) and ARM9 (400 MHz) takes 10 seconds and one hour each to process a frame.

• Journal of applied mathematics & informatics
• /
• v.32 no.5_6
• /
• pp.621-633
• /
• 2014

In this paper, we introduce a general iterative algorithm for asymptotically quasi-${\phi}$-nonexpansive mappings in the intermediate sense to have the strong convergence in the framework of Banach spaces. The results presented in the paper improve and extend the corresponding results announced by many authors.

• Journal of the Korean Society for Precision Engineering
• /
• v.12 no.1
• /
• pp.123-131
• /
• 1995

다주파수 입력을 갖는 강한 비선형 시스템의 유사주기 (quasi-periodic) 해를 해석하기 위하여 개선된 고정 점법(FPA:Fixed Point Alogrithm)을 개발하였다. 안정성 및 천이 특성을 판별하기 위하여 사용되어지는 Floquest 지수인 해석적 자코비언을 구하기 위하여 Poincare 맵상에서 이산 적분법을 새로이 고안, 사용하였다. 본 방법의 우수성을 입증하기 위하여 2개의 주파수 입력을 갖는 선형 시스템과 비선형 시스템을 예로 사용하였다. 본 방법을 이용하여 비선형 시스템에서 발생한 복잡한 chaos 현상을 체계적으로 해석하였다.

• Journal of the Korean Mathematical Society
• /
• v.34 no.1
• /
• pp.1-12
• /
• 1997

Complementaity problem theory developed by Lemke [10], Cottle and Dantzig [8] and others in the early 1960s and thereafter, has numerous applications in diverse fields of mathematical and engineering sciences. And it is closely related to variational inquality theory and fixed point theory. Recently, fixed point methods for the solving of nonlinear complementarity problems were considered by Noor et al. [11, 12]. Also complementarity problems related to variational inequality problems were investigated by Chang [1], Cottle [7] and others.

• Kyungpook Mathematical Journal
• /
• v.62 no.1
• /
• pp.69-88
• /
• 2022

In this work, the three-step intermixed iteration for two finite families of nonlinear mappings is introduced. We prove a strong convergence theorem for approximating a common fixed point of a strict pseudo-contraction and strictly pseudononspreading mapping in a Hilbert space. Some additional results are obtained. Finally, a numerical example in a space of real numbers is also given and illustrated.

• Journal of Power Electronics
• /
• v.11 no.2
• /
• pp.194-201
• /
• 2011

The air flow supplied to a fuel cell system is one of the most significant factors in determining fuel efficiency. The conventional method of controlling the air flow is to fix the oxygen supply at an estimated constant rate for optimal efficiency. However, the actual optimal point can deviated from the pre-set value due to temperature, load conditions and so on. In this paper, the maximum efficiency point tracking (MEPT) algorithm is proposed for finding the optimal air supply rate in real time to maximize the net-power generation of fuel cell systems. The fixed step MEPT algorithm has slow dynamics, thus it affects the overall efficiency. As a result, the variable step MEPT algorithm is proposed to compensate for this problem instead of a fixed one. The complete small signal model of a PEM Fuel cell system is developed to perform a stability analysis and to present a design guideline. For a design example, a 1kW PEM fuel cell system with a DSP 56F807 (Motorola Inc) was built and tested using the proposed MEPT algorithm. This control algorithm is very effective for a soft current change load like a grid connected system or a hybrid electric vehicle system with a secondary energy source.

• Journal of the Korean Mathematical Society
• /
• v.52 no.6
• /
• pp.1179-1194
• /
• 2015

In this paper, we introduce a new iterative algorithm for finding a common element of the set of solutions of a generalized mixed equilibrium problem related to a continuous monotone mapping, the set of solutions of a variational inequality problem for a continuous monotone mapping, and the set of fixed points of a continuous pseudocontractive mapping in Hilbert spaces. Weak convergence for the proposed iterative algorithm is proved. Our results improve and extend some recent results in the literature.

• Bulletin of the Korean Mathematical Society
• /
• v.53 no.6
• /
• pp.1831-1844
• /
• 2016

In this paper, we improve the full-Newton step infeasible interior-point algorithm proposed by Mansouri et al. [6]. The algorithm takes only one full-Newton step in a major iteration. To perform this step, the algorithm adopts the largest logical value for the barrier update parameter ${\theta}$. This value is adapted with the value of proximity function ${\delta}$ related to (x, y, s) in current iteration of the algorithm. We derive a suitable interval to change the parameter ${\theta}$ from iteration to iteration. This leads to more flexibilities in the algorithm, compared to the situation that ${\theta}$ takes a default fixed value.

• Proceedings of the KIEE Conference
• /
• 2004.11c
• /
• pp.647-649
• /
• 2004

When a controller is implemented by a one-chip processor with fixed-point operations, the finite alphabet problem usually occurs since parameters and signals should be taken in a finite set of values. This paper formulates PID finite alphabet PID control problem which combines the PID controller with the finite alphabet problem. We will propose a PID parameter tuning method based on an optimization algorithm under the finite alphabet condition. The PID parameters can be represented by a fixed-point representation, and then the problem is formulated as an optimization with constraints that parameters are taken in the finite set. Some simulation are to be performed to exemplify the performance of the PID parameter tuning method proposed in this paper.