• Title/Summary/Keyword: 다항함수(多項函數)

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Parallelized PI($\pi$) Calculation Algorithm using MPI (MPI를 활용한 PI($\pi$)값 계산 병렬화 알고리즘)

  • Choi, Min;Maeng, Seung-Ryoul
    • Proceedings of the Korean Information Science Society Conference
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    • pp.91-93
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    • 2004
  • 정확한 $\pi$값의 계산은 자연과학의 여러 분야에 도움을 준다 이와 같이 $\pi$값을 계산하는 여러 가지 방법이 제안되어 있으며 널리 사용되고 있으나, 본 논문에서는 MPI 라이브러리를 활용한 $\pi$값 계산의 병렬화 알고리즘을 소개한다. tan$^{-1}$($\chi$)의 정의를 이용하는 $\pi$값 계산 방법은 다항식의 계산과정에서 각 항(term)들의 종속성으로 인하여 병렬화 수행이 힘든 단점이 있다. 본 논문에서는 tan$^{-1}$($\chi$)를 맥클로린 수열(Maclaurin Series)을 통하여 다항함수로 표현하고, 병렬화 수행에 적합한 적분형태로 변형한다. 따라서. MPI 환경에서 수행하기 적합한 $\pi$값 계산의 병렬화 알고리즘을 제안하고 8노드 클러스터 환경에서 성능을 비교해본다. 또한, 직렬화된 방법에 대한 성능향상(speedup)을 측정한다.

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Flexural Vibrations Of Simply Supported Sectorial Plates with Simply Supported And Free Radial Edges (단순지지와 자유의 방사연단을 갖는 단순지지 부채꼴형 평판의 휨진동)

  • Han, Bong-Koo;Kim, Joo-Woo
    • Journal of the Korea institute for structural maintenance and inspection
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    • v.2 no.4
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    • pp.217-223
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    • 1998
  • 본 논문에서는 원형연단이 단순지지 되어 있을 때 단순과 자유의 방사연단 조건을 갖는 부채꼴형 평판의 휨진동에 대한 엄밀한 해석방법을 제시한다. Ritz방법을 이용하여 수직진동변위를 두가지 적합 함수식으로 가정하였다. 이러한 두가지의 적합 함수식은 (1) 수학적으로 완전한 대수삼각다항함수와, (2) 둔각 모서리에서의 휨모멘트 특이도를 고려하는 모서리함수로 구성되어있다. 본 연구에서는 방사연단의 둔각 모서리를 이루는 부채꼴형 각도의 범위에 따른 엄밀한 진동수 및 수직진동 변위의 전형적인 등고선을 제시하였다.

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Mathematical Structures of Polynomials in Jeong Yag-yong's Gugo Wonlyu (정약용(丁若鏞)의 산서(算書) 구고원류(勾股源流)의 다항식(多項式)의 수학적(數學的) 구조(構造))

  • Hong, Sung Sa;Hong, Young Hee;Lee, Seung On
    • Journal for History of Mathematics
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    • v.29 no.5
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    • pp.257-266
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    • 2016
  • This paper is a sequel to our paper [3]. Although polynomials in the tianyuanshu induce perfectly the algebraic structure of polynomials, the tianyuan(天元) is always chosen by a specific unknown in a given problem, it can't carry out the role of the indeterminate in ordinary polynomials. Further, taking the indeterminate as a variable, one can study mathematical structures of polynomials via those of polynomial functions. Thus the theory of polynomials in East Asian mathematics could not be completely materialized. In the previous paper [3], we show that Jeong Yag-yong disclosed in his Gugo Wonlyu(勾股源流) the mathematical structures of Pythagorean polynomials, namely polynomials p(a, b, c) where a, b, c are the three sides gou(勾), gu(股), xian(弦) of a right triangle, respectively. In this paper, we show that Jeong obtained his results through his recognizing Pythagorean polynomials as polynomial functions of three variables a, b, c.

On Energy-Optimal Voltage Scheduling for Fixed-Priority Hard Real-Time Systems (고정 우선순위 경성 실시간 시스템에 대한 최적의 전압 스케줄링)

  • 윤한샘;김지홍
    • Journal of KIISE:Computer Systems and Theory
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    • v.31 no.10
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    • pp.562-574
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    • 2004
  • We address the problem of energy-optimal voltage scheduling for fixed-priority hard real-time systems. First, we prove that the problem is NP-hard. Then, we present a fully polynomial time approximation scheme (FPTAS) for the problem. for any $\varepsilon$>0, the proposed approximation scheme computes a voltage schedule whose energy consumption is at most (1+$\varepsilon$) times that of the optimal voltage schedule. Furthermore, the running time of the proposed approximation scheme is bounded by a polynomial function of the number of input jobs and 1/$\varepsilon$. Experimental results show that the approximation scheme finds more efficient voltage schedules faster than the best existing heuristic.

The Assessing Comparative Study for Statistical Process Control of Software Reliability Model Based on polynomial hazard function (다항 위험함수에 근거한 NHPP 소프트웨어 신뢰모형에 관한 통계적 공정관리 접근방법 비교연구)

  • Kim, Hee-Cheul;Shin, Hyun-Cheul
    • The Journal of Korea Institute of Information, Electronics, and Communication Technology
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    • v.8 no.5
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    • pp.345-353
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    • 2015
  • There are many software reliability models that are based on the times of occurrences of errors in the debugging of software. It is shown that it is possible to do parameter inference for software reliability models based on finite failure model and non-homogeneous Poisson Processes (NHPP). For someone making a decision to market software, the conditional failure rate is an important variables. In this case, finite failure model are used in a wide variety of practical situations. Their use in characterization problems, detection of outlier, linear estimation, study of system reliability, life-testing, survival analysis, data compression and many other fields can be seen from the many study. Statistical process control (SPC) can monitor the forecasting of software failure and thereby contribute significantly to the improvement of software reliability. Control charts are widely used for software process control in the software industry. In this paper, proposed a control mechanism based on NHPP using mean value function of polynomial hazard function.

Evolutionarily Optimized Design of Self-Organized Fuzzy Polynomial Neural Networks by Means of Dynamic Search Method of Genetic Algorithms (유전자 알고리즘의 동적 탐색 방법을 이용한 자기구성 퍼지 다항식 뉴럴 네트워크의 진화론적 최적화 설계)

  • Park Ho-Sung;Oh Sung-Kwun;Ahn Tae-Chon
    • Proceedings of the Korean Institute of Intelligent Systems Conference
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    • pp.475-478
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    • 2005
  • 본 논문에서는 자기구성 퍼지다항식 뉴럴 네트워크(SOFPNN)를 구성하고 있는 퍼지 다항식뉴론(FPM)의 구조와 파라미터를 유전자 알고리즘을 이용하여 최적화시킨 새로운 개념의 진화론적 최적 고급 자기구성 퍼지 다항식 뉴릴 네트워크를 소개한다. 기존의 자기구성 퍼지 다항식 뉴럴 네트워크에서 모델을 설계할 때에는 설계자의 주관적인 특징과 시행착오에 의해서 모델을 구축하였다. 이러한 설계자의 경험을 배제하고 객관적이고 효율적인 모델을 구축하기 위해서 본 논문에서는 FPH의 파라미터들을 최적화 알고리즘인 유전자 알고리즘을 이용하여 동조하였다. 즉, 모델을 구축하는데 기본이 되는 FPN의 각각의 파라미터들-입력변수의 수, 다항식 차수, 입력변수, 멤버쉽 함수의 수, 그리고 멤버쉽 함수의 정점-을 동조함으로써 기존의 모델에 비해서 구조적으로 그리고 파라미터적으로 최적화된 네트워크를 생성할 수 있다. 뿐만 아니라 주어진 데이터의 특성을 모델 구축에 반영하고자 멤버쉽 함수의 정점 역시 유전자 알고리즘으로 동조하였다. 실험적 예제를 통하여 제안된 모델의 성능을 확인한 결과 기존의 퍼지모델 및 신경망 모델에 비해서 아주 우수한 근사화 능력과 일반화 능력을 가짐을 알 수 있다.

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Improved Valve-Point Optimization Algorithm for Economic Load Dispatch Problem with Non-convex Fuel Cost Function (비볼록 발전비용함수 경제급전문제의 개선된 밸브지점 최적화 알고리즘)

  • Lee, Sang-Un
    • The Journal of the Institute of Internet, Broadcasting and Communication
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    • v.15 no.6
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    • pp.257-266
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    • 2015
  • There is no polynomial-time algorithm that can be obtain the optimal solution for economic load dispatch problem with non-convex fuel cost functions. Therefore, electrical field uses quadratic fuel cost function unavoidably. This paper proposes a valve-point optimization (VPO) algorithm for economic load dispatch problem with non-convex fuel cost functions. This algorithm sets the initial values to maximum powers $P_i{\leftarrow}P_i^{max}$ for each generator. It then reduces the generation power of generator i with an average power cost of $_{max}\bar{c}_i$ to a valve point power $P_{ik}$. The proposed algorithm has been found to perform better than the extant heuristic methods when applied to 13 and 40-generator benchmark data. This paper consequently proves that the optimal solution to economic load dispatch problem with non-convex fuel cost functions converges to the valve-point power of each generator.

Study on the Capacity Design Tool Development for Open-loop Ground Heat Exchanger (개방형 지중열교환기 용량 설계 방법에 관한 연구)

  • Ryu, Hyung-Kyou;Choi, Seung-Hyuck;Yun, Hi-won;Gim, Yu-Seung
    • Journal of the Korean Society for Geothermal and Hydrothermal Energy
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    • v.13 no.2
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    • pp.9-15
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    • 2017
  • When applying geothermal systems in cities such as seoul where high density development prevails, the selection of geothermal system capable of obtaining a large capacity in the limited grounds is necessary. In this study, an easy-to-use design tool is developed in the form of spreadsheet by applying the calculation theory of existing closed-loop vertical ground heat exchanger that can be used in the early design stage of the open-loop ground heat exchanger. By only using the maximum cooling and heating load, it is possible to calculate optimal design open-loop ground heat exchanger. Further research is needed, we are plan to improve the program considering the heat loss of groundwater flowing in the inner casing, G-Function for Open-Loop, and verification by applying actual projects.

Proposition of polytomous discrimination index and test statistics (다항판별지수와 검정통계량 제안)

  • Choi, Jin Soo;Hong, Chong Sun
    • Journal of the Korean Data and Information Science Society
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    • v.27 no.2
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    • pp.337-351
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    • 2016
  • There exist many real situations that statistical decision problems are classified into more than two categories. In these cases, the concordance statistics by the pair approach are mostly used. However, the expression of the classification of categories are ambiguous. Recently, the standardized evaluation data and re-expressed concordance statistics are defined and could be explained their meanings. They have still some non-specific problems for standard criteria of the statistics. Since these can be considered between result and truth categories additionally, two alternative concordance statistics might be proposed in this paper. Some advantages are founded that the proposed statistics could be discriminated all possible cases for two randomly selected categories. Moreover since the proposed statistics are represented with indicator functions, these could be transformed non-parametrically, so that these concordances are used for hypothesis testing.

A LOGIT based Traffic Assignment Model Considering Passenger Transfer on Railway Network (철도 네트워크에서 환승수요를 고려한 다항로짓 기반 통행배정 모형 연구)

  • Park, Bum-Hwan;Rho, Hag-Lae;Cheon, Seung-Hoon;Lee, Jin-Sun
    • Journal of the Korean Society for Railway
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    • v.14 no.3
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    • pp.276-284
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    • 2011
  • In our study, we present a new LOGIT-based traffic assignment model applicable to intercity railway network. Most traffic assignment models have been developed for public transit assignment in urban area, so that they are known to produce unrealistic results in intercity railway demand analysis. Especially, since the introduction of KTX, more passengers are using a route including KTX service and the schedule becomes more compatible with transfer. Our study presents a new LOGIT-based traffic assignment model considering passenger transfer. To do so, we suggest a new route search algorithm to find K paths with non increasing order in the utility value.