• 한국수학교육학회지시리즈E:수학교육논문집
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• 제29권1호
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• pp.1-18
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• 2015

수학교육에서 학생들의 수감각 발달을 강조하고 있지만 이에 대한 연구는 부족한 실정이며 초등학생에 국한된 경우가 많다. 이에 본 연구는 초등학생과 중학생을 대상으로 수감각 문제를 해결하는 방법을 분석함으로써, 수감각 지도방향에 대한 시사점을 제공하고자 하였다. 이를 위해 본 연구에서는 문제를 해결하는 방법으로 수감각을 활용하는 방법과 알고리즘을 활용하는 방법으로 분류하고, 검사지를 이용하여 학생들의 반응을 분석하였다. 그 결과 중학생들이 초등학생들에 비해 수감각 검사 점수가 높았으며, 문제해결 방법 중 수감각을 활용하는 비율도 높았다. 또한 성취도가 높은 학생들은 수감각과 알고리즘을 모두 활용하였으나 성취도가 낮은 학생들은 알고리즘을 활용하여 문제를 해결하려고 하는 경향이 강했다. 그리고 성취도가 높은 학생들은 초등학생에 비해 중학생이 상대적으로 수감각을 더 많이 활용하였으나, 성취도가 낮은 학생들끼리는 차이가 없었다. 마지막으로 수감각 구성 요소별로 수감각을 활용하는 비율에 차이가 있는 것으로 나타났다.

• 정보교육학회논문지
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• 제16권1호
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• pp.11-20
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• 2012

프로그래밍의 핵심은 어디까지나 알고리즘 학습에 있으며 이를 통한 창의적이고 논리적인 문제해결력의 향상이 프로그래밍 학습의 목표인 것이다. 그렇다면 어떤 알고리즘들을 어떠한 순서대로 가르치는가에 대한 고민을 좀 더 해 볼 필요가 있으며 그 효과성에 대해서도 연구해 볼 필요가 있을 것이다. 본 연구는 개념적 알고리즘의 내용들을 한국정보올림피아드 초등부 경시부문의 문제들을 이용하여 학습할 수 있도록 알고리즘 학습 교재를 개발하고 이 효과를 검증하였다.

• Journal of applied mathematics & informatics
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• 제26권1_2호
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• pp.213-222
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• 2008

Iterative methods are often suitable for solving least squares problems min$||Ax-b||_2$, where A $\epsilon\;\mathbb{R}^{m{\times}n}$ is large and sparse. The well known LSQR algorithm is among the iterative methods for solving these problems. A good preconditioner is often needed to speedup the LSQR convergence. In this paper we present the numerical experiments of applying a well known preconditioner for the LSQR algorithm. The preconditioner is based on the $A^T$ A-orthogonalization process which furnishes an incomplete upper-lower factorization of the inverse of the normal matrix $A^T$ A. The main advantage of this preconditioner is that we apply only one of the factors as a right preconditioner for the LSQR algorithm applied to the least squares problem min$||Ax-b||_2$. The preconditioner needs only the sparse matrix-vector product operations and significantly reduces the solution time compared to the unpreconditioned iteration. Finally, some numerical experiments on test matrices from Harwell-Boeing collection are presented to show the robustness and efficiency of this preconditioner.

• 한국철도학회논문집
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• 제9권2호
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• pp.206-211
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• 2006

This thesis presents railroad crew restoring problem, which is to determine the railroad plan allocation. This problem is constructed that determine the sequence of duties that railroad crews have to perform. We analyze characteristic of this problem and railroad industry. It's hard to consider many constraint conditions. We propose Integer Programming model and easy methodology to be considered all given operation rules. This problem is known to be NP-hard. We develop a genetic algorithm, which is proved to be powerful in solving optimization problems. We proposed the effective mathematical model and algorithm about making crew restoring in real industry.

• Journal of Multimedia Information System
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• 제4권4호
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• pp.219-224
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• 2017

This paper is to introduce an application of face recognition algorithm in parallel. We have experiments of 25 images with different motions and simulated the image recognitions; grouping of the image vectors, image normalization, calculating average image vectors, etc. We also discuss an analysis of the related eigen-image vectors and a parallel algorithm. To develop the parallel algorithm, we propose a new type of initial matrices for eigenvalue problem. If A is a symmetric matrix, initial matrices for eigen value problem are investigated: the "optimal" one, which minimize ${\parallel}C-A{\parallel}_F$ and the "super optimal", which minimize ${\parallel}I-C^{-1}A{\parallel}_F$. In this paper, we present a general new approach to the design of an initial matrices to solving eigenvalue problem based on the new optimal investigating C with preserving the characteristic of the given matrix A. Fast all resulting can be inverted via fast transform algorithms with O(N log N) operations.

• 전기학회논문지
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• 제56권10호
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• pp.1699-1708
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• 2007

The optimal power flow(OPF) problem was introduced by Carpentier in 1962 as a network constrained economic dispatch problem. Since then, the OPF problem has been intensively studied and widely used in power system operation and planning. In these days, OPF is becoming more and more important in the deregulation environment of power pool and there is an urgent need of faster solution technique for on-line application. To solve OPF problem, many heuristic optimization methods have been developed, such as Genetic Algorithm(GA), Evolutionary Programming(EP), Evolution Strategies(ES), and Particle Swarm Optimization(PSO). Especially, PSO algorithm is a newly proposed population based heuristic optimization algorithm which was inspired by the social behaviors of animals. However, population based heuristic optimization methods require higher computing time to find optimal point. This shortcoming is overcome by a straightforward parallel processing of PSO algorithm. The developed parallel PSO algorithm is implemented on a PC cluster system with 6 Intel Pentium IV 2GHz processors. The proposed approach has been tested on the IEEE 30-bus system. The results showed that computing time of parallelized PSO algorithm can be reduced by parallel processing without losing the quality of solution.

• Management Science and Financial Engineering
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• 제11권2호
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• pp.85-103
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• 2005

In this paper, we consider the routing and wavelength assignment problem in survivable WDM transport network without wavelength conversion. We assume the single-link failure and a path protection scheme in optical layer. When a physical network and a set of working paths are given, the problem is to select a link-disjoint protection path for each working path and assign a wavelength for each working and protection path. We give an integer programming formulation of the problem and propose an algorithm to solve it. Though the formulation has exponentially many variables, we solve the linear programming relaxation of it by using column generation technique. We devise a branch-and price algorithm to solve the column generation problem. After solving the linear programming relaxation, we apply a variable fixing procedure combined with the column generation to get an integral solution. We test the proposed algorithm on some randomly generated data and test results show that the algorithm gives very good solutions.

• 대한수학회지
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• 제59권2호
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• pp.311-335
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• 2022

This paper treats Merton's classical portfolio optimization problem for a market participant who invests in safe assets and risky assets to maximize the expected utility. When the state process is a d-dimensional Markov diffusion, this problem is transformed into a problem of solving a Hamilton-Jacobi-Bellman (HJB) equation. The main purpose of this paper is to solve this HJB equation by a deep learning algorithm: the deep Galerkin method, first suggested by J. Sirignano and K. Spiliopoulos. We then apply the algorithm to get the solution to the HJB equation and compare with the result from the finite difference method.

• Journal of applied mathematics & informatics
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• 제28권5_6호
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• pp.1239-1248
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• 2010

In this paper, an implementable BFGS bundle algorithm for solving a nonsmooth convex optimization problem is presented. The typical method minimizes an approximate Moreau-Yosida regularization using a BFGS algorithm with inexact function and the approximate gradient values which are generated by a finite inner bundle algorithm. The approximate subgradient of the objective function is used in the algorithm, which can make the algorithm easier to implement. The convergence property of the algorithm is proved under some additional assumptions.

• Journal of applied mathematics & informatics
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• 제7권1호
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• pp.215-222
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• 2000

A multigrid algorithm is developed for solving the one- dimensional initial boundary value problem. The numerical solutions of linear and nonlinear Burgers; equation for various initial conditions are studied. The stability conditions are derived by Von -Neumann analysis . Numerical results are presented.