• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.13 no.1
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• pp.41-53
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• 2009

A primal-dual interior point method(IPM) not only is the most efficient method for a computational point of view but also has polynomial complexity. Most of polynomialtime interior point methods(IPMs) are based on the logarithmic barrier functions. Peng et al.([14, 15]) and Roos et al.([3]-[9]) proposed new variants of IPMs based on kernel functions which are called self-regular and eligible functions, respectively. In this paper we define a new kernel function and propose a new IPM based on this kernel function which has $O(n^{\frac{2}{3}}log\frac{n}{\epsilon})$ and $O(\sqrt{n}log\frac{n}{\epsilon})$ iteration bounds for large-update and small-update methods, respectively.

• The Pure and Applied Mathematics
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• v.19 no.1
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• pp.59-71
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• 2012

In this paper, we prove the stability in random normed spaces via fixed point method for the functional equation $$f(x+y+z)-f(x+y)-f(y+z)-f(x+z)+f(x)+f(y)+f(z)=0$$. by using a fixed point theorem in the sense of L. C$\breve{a}$dariu and V. Radu.

• Korean Journal of Mathematics
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• v.20 no.1
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• pp.19-31
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• 2012

In this paper, we prove the stability in random normed spaces via fixed point method for the functional equation $$2f(x+y)+f(x-y)+f(y-x)-f(2x)-f(2y)=0$$.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.1
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• pp.51-63
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• 2012

In this paper, we prove the stability in random normed spaces via fixed point method for the functional equation $$f(2x+y)+f(2x-y)+2f(x)-f(x+y)-f(x-y)-2f(2x)=0$$.

• Journal of Information Processing Systems
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• v.16 no.1
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• pp.120-131
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• 2020

In order to solve the problem of point clouds coordinate conversion of non-directional scanners, this paper proposes a basic Rodrigues rotation method. Specifically, we convert the 6 degree-of-freedom (6-DOF) rotation and translation matrix into the uniaxial rotation matrix, and establish the equation of objective vector conversion based on the basic Rodrigues rotation scheme. We demonstrate the applicability of the new method by using a bar-shaped emboss point clouds as experimental input, the three-axis error and three-term error as validate indicators. The results suggest that the new method does not need linearization and is suitable for optional rotation angle. Meanwhile, the new method achieves the seamless splicing of point clouds. Furthermore, the coordinate conversion scheme proposed in this paper performs superiority by comparing with the iterative closest point (ICP) conversion method. Therefore, the basic Rodrigues rotation method is not only regarded as a suitable tool to achieve the conversion of point clouds, but also provides certain reference and guidance for similar projects.

• Proceedings of the KIEE Conference
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• 2007.04a
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• pp.26-28
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• 2007

The motion estimation is the most important technique in the image compression of the video standards. In the case of next generation standards in the video codec as H.264, a high compression-efficiency can be also obtained by using a motion compensation. To obtain the accurate motion search, a motion estimation should be achieved up to 1/2 pixel and 1/4 pixel uiuts. To do this, the computational complexity is increased although the image compression rate is increased. Therefore, in this paper, we propose the advanced sub-pixel block matching algorithm to reduce the computational complexity by using a statistical characteristics of SAD(Sum of Absolute Difference). Generally, the probability of the minimum SAD values is high when searching point is in the distance 1 from the reference point. Thus, we reduced the searching area and then we can overcome the computational complexity problem. The main concept of proposed algorithm, which based on TSS(Three Step Search) method, first we find three minimum SAD points which is in integer distance unit, and then, in second step, the optimal point is in 1/2 pixel unit either between the most minimum SAD value point and the second minimum SAD point or between the most minimum SAD value point and the third minimum SAD point In third step, after finding the smallest SAD value between two SAD values on 1/2 pixel unit, the final optimized point is between the most minimum SAD value and the result value of the third step, in 1/2 pixel unit i.e., 1/4 pixel unit in totally. The conventional TSS method needs an eight.. search points in the sub-pixel steps in 1/2 pixel unit and also an eight search points in 1/4 pixel, to detect the optimal point. However, in proposed algorithm, only total five search points are needed. In the result. 23 % improvement of processing speed is obtained.

• The Journal of Korea Robotics Society
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• v.17 no.3
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• pp.373-380
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• 2022

This paper considers a method of fast correspondence matching for iterative closest point (ICP) algorithm. In robotics, the ICP algorithm and its variants have been widely used for pose estimation by finding the translation and rotation that best align two point clouds. In computational perspectives, the main difficulty is to find the correspondence point on the reference point cloud to each observed point. Jump-table-based correspondence matching is one of the methods for reducing computation time. This paper proposes a method that corrects errors in an existing jump-table-based correspondence matching algorithm. The criterion activating the use of jump-table is modified so that the correspondence matching can be applied to the situations, such as point-cloud registration problems with highly curved surfaces, for which the existing correspondence-matching method is non-applicable. For demonstration, both hardware and simulation experiments are performed. In a hardware experiment using Hokuyo-10LX LiDAR sensor, our new algorithm shows 100% correspondence matching accuracy and 88% decrease in computation time. Using the F1TENTH simulator, the proposed algorithm is tested for an autonomous driving scenario with 2D range-bearing point cloud data and also shows 100% correspondence matching accuracy.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.15 no.7
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• pp.2610-2630
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• 2021

The aim of this paper is to propose the alternative algorithm to finish the process in public key cryptography. In general, the proposed method can be selected to finish both of modular exponentiation and point multiplication. Although this method is not the best method in all cases, it may be the most efficient method when the condition responds well to this approach. Assuming that the binary system of the exponent or the multiplier is considered and it is divided into groups, the binary system is in excellent condition when the number of groups is small. Each group is generated from a number of 0 that is adjacent to each other. The main idea behind the proposed method is to convert the exponent or the multiplier as the subtraction between two integers. For these integers, it is impossible that the bit which is equal to 1 will be assigned in the same position. The experiment is split into two sections. The first section is an experiment to examine the modular exponentiation. The results demonstrate that the cost of completing the modular multiplication is decreased if the number of groups is very small. In tables 7 - 9, four modular multiplications are required when there is one group, although number of bits which are equal to 0 in each table is different. The second component is the experiment to examine the point multiplication process in Elliptic Curves Cryptography. The findings demonstrate that if the number of groups is small, the costs to compute point additions are low. In tables 10 - 12, assigning one group is appeared, number of point addition is one when the multiplier of a point is an even number. However, three-point additions are required when the multiplier is an odd number. As a result, the proposed method is an alternative way that should be used when the number of groups is minimal in order to save the costs.

• Korea-Australia Rheology Journal
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• v.16 no.1
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• pp.1-15
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• 2004

The computation of viscoelastic flow using neural networks and stochastic simulation (CVFNNSS) is developed from the point of view of Eulerian CONNFFESSIT (calculation of non-Newtonian flows: finite elements and stochastic simulation techniques). The present method is based on the combination of radial basis function networks (RBFNs) and Brownian configuration fields (BCFs) where the stress is computed from an ensemble of continuous configuration fields instead of convecting discrete particles, and the velocity field is determined by solving the conservation equations for mass and momentum with a finite point method based on RBFNs. The method does not require any kind of element-type discretisation of the analysis domain. The method is verified and its capability is demonstrated with the start-up planar Couette flow, the Poiseuille flow and the lid driven cavity flow of Hookean and FENE model materials.

• Journal of the Korean Society for Precision Engineering
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• v.32 no.11
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• pp.983-988
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• 2015

This paper details a new ultra-precise turning method for increasing surface quality, "Multi Point B Axis Control Method." Machined surface error is minimized by the compensation machining process, but the process leaves residual chip marks and surface roughness. This phenomenon is unavoidable in the diamond turning process using existing machining methods. However, Multi Point B axis control uses a small angle (< $1^{\circ}$) for the unused diamond edge for generation of ultra-fine surfaces; no machining chipping occurs. It is achieved by compensated surface profiling via alignment of the tool radial center on the center of the B axis rotation table. Experimental results show that a diamond turned surface using the Multi Point B axis control method achieved P-V $0.1{\mu}m$ and Ra 1.1nm and these ultra-fine surface qualities are reproducible.