• 대한수학회논문집
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• 제12권1호
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• pp.69-73
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• 1997

We show that if T is an $\varepsilon$-approximate Jordan functional such that T(a) = 0 implies $T(a^2) = 0 (a \in A)$ then T is continuous and $\Vert T \Vert \leq 1 + \varepsilon$. Also we prove that every $\varepsilon$-near Jordan mapping is an $g(\varepsilon)$-approximate Jordan mapping where $g(\varepsilon) \to 0$ as $\varepsilon \to 0$ and for every $\varepsilon > 0$ there is an integer m such that if T is an $\frac {\varepsilon}{m}$-approximate Jordan mapping on a finite dimensional Banach algebra then T is an $\varepsilon$-near Jordan mapping.

• 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.

• 정보과학회 논문지
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• 제44권8호
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• pp.760-766
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• 2017

반복적인 문자열은 데이터압축, 생물정보학 등 여러 분야에서 연구되어 왔다. 본 논문에서는 음악서열이나 주가지수와 같이 정수로 표현될 수 있는 문자열에 대한 반복에 대해 연구한다. 최근 정수문자열의 최소 ${\delta}$-근사주기와 최소 ${\gamma}$-근사주기를 찾는 문제들이 소개되었고, 문자열의 길이가 n일 때, 두 문제를 각각 $O(n^2)$ 시간에 해결하는 알고리즘들이 제시되었다. 본 논문에서는 위의 두 문제에 대해 각각 $O(n^2)$개의 스레드를 이용하여 O(n) 시간에 해결하는 병렬알고리즘을 제시한다. 실험결과, n = 10,000일 때, 본 논문에서 제시하는 병렬알고리즘은 순차알고리즘보다 최소 ${\delta}$-근사주기를 계산하는데 약 19.7배, 최소 ${\gamma}$-근사주기를 계산하는데 약 40.08배 빠른 수행시간을 보였다.

• Journal of applied mathematics & informatics
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• 제27권1_2호
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• pp.149-159
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• 2009

In this paper, we introduce some approximate optimal solutions and an augmented Lagrangian function in nonlinear programming, establish dual function and dual problem based on the augmented Lagrangian function, discuss the relationship between the approximate optimal solutions of augmented Lagrangian problem and that of primal problem, obtain approximate KKT necessary optimality condition of the augmented Lagrangian problem, prove that the approximate stationary points of augmented Lagrangian problem converge to that of the original problem. Our results improve and generalize some known results.

• 대한수학회보
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• 제41권2호
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• pp.257-267
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• 2004

In this paper, we introduce, for each approximate distribution $\~{T}$ of [a, b], the approximate Henstock-Stieltjes integral with value in Banach spaces. The Henstock integral is a special case of this where $\~{T}\;=\;\{(\tau,\;[a,\;b])\;:\;{\tau}\;{\in}\;[a,\;b]\}$. This new concept generalizes Henstock integral and abstract Perron-Stieltjes integral. We establish a uniform convergence theorem for approximate Henstock-Stieltjes integral, which is an improvement of the uniform convergence theorem for Perron-Stieltjes integral by Schwabik [3].

• 한국소성가공학회:학술대회논문집
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• 한국소성가공학회 1999년도 춘계학술대회논문집
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• pp.71-75
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• 1999

An approximate similarity theory has been applied to predict the forming load of non-axisymmetric forging of aluminum alloys through model material tests. The approximate similarity theory is applicable when strain rate sensitivity geometrical size and die velocity of model materials are different from those of real materials. Actually the forming load of yoke which is an automobile part made of aluminum alloys(Al-6061) is predicted by using this approximate similarity theory. Firstly upset forging tests are have been carried out to determine the flow curves of three model materials and aluminum alloy(Al-6061) and a suitable model material is selected for model material test of Al-6061 And then and forging tests of aluminum yokes have been performed to verify the forming load predicted from the model material which has been selected from above upset forging tests, The forming loads of aluminum yoke forging predicted by this approximate similarity theory are in good agreement with the experimental results of Al-6061 and the results of finite element analysis using DEFORM-3D.

• Journal of Mechanical Science and Technology
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• 제16권4호
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• pp.501-511
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• 2002

This paper presents a study of the effect of rolling temperature, roll gap (pass height), initial specimen size and steel grades of specimens on the roll force in round-oval-round pass sequence by applying approximate method and verifications through single stand pilot rod rolling tests. The results show that the predicted roll forces are in good agreement with the experimentally measured ones. The approximate model is independent of the change of roll gap, specimen size and temperature. Thus, the generality of the prediction methodology employed in the approximate model is proven. This study also demonstrates that Shida's constitutive equation employed in the approximate model needs to be corrected somehow to be applicable for the medium and high carbon steels in a lower temperature interval (700∼900$\^{C}$).

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2007년도 정기 학술대회 논문집
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• pp.141-144
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• 2007

Given a number of training data, a traditional BPN is normally trained by minimizing the absolute difference between target outputs and approximate outputs. When BPN is used as a meta-model for inequality constraint function, approximate optimal solutions are sometimes actually infeasible in a case where they are active at the constraint boundary. The paper describes the development of the efficient BPN based meta-model that enhances the constraint feasibility of approximate optimal solution. The modified BPN based meta-model is obtained by including the decision condition between lower/upper bounds of a constraint and an approximate value. The proposed approach is verified through a simple mathematical function and a ten-bar planar truss problem.

• ETRI Journal
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• 제43권4호
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• pp.684-693
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• 2021

This paper presents a low-cost two-stage approximate multiplier for bfloat16 (brain floating-point) data processing. For cost-efficient approximate multiplication, the first stage implements Mitchell's algorithm that performs the approximate multiplication using only two adders. The second stage adopts the exact multiplication to compensate for the error from the first stage by multiplying error terms and adding its truncated result to the final output. In our design, the low-cost multiplications in both stages can reduce hardware costs significantly and provide low relative errors by compensating for the error from the first stage. We apply our approximate multiplier to the convolutional neural network (CNN) inferences, which shows small accuracy drops with well-known pre-trained models for the ImageNet database. Therefore, our design allows low-cost CNN inference systems with high test accuracy.

• 대한기계학회논문집A
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• 제34권11호
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• pp.1603-1611
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• 2010

본 논문에서는 범프 및 브레이크 하중조건 하에서 자동차 넉클의 강도설계에 관한 다양한 회귀모델 기반 근사최적화 기법 및 그 성능을 비교하고자 한다. 최적설계문제는 응력, 변형 및 진동주파수의 제한조건 하에서 중량을 최소화하여 설계변수인 단면치수가 결정되도록 정식화 된다. 비교 연구를 위해 사용된 근사화 기법은 순차적 근사최적화(SAO), 순차적 이점대각이차 근사최적화(STDQAO), 그리고 개선된 이동최소 자승법(MLSM) 기반 근사최적화 기법인 CF-MLSM 와 Post-MLSM 이다. SAO 와 STDQAO 적용을 위하여 상용 프로세스통합 설계최적화(PIDO) 코드를 사용하였다. 본 연구에 적용한 MLSM 기반 근사최적화 기법들은 제한조건의 가용성을 보장할 수 있도록 새롭게 개발되었다. 다양한 근사최적화 기법에 의한 설계결과는 설계 해의 개선 및 수렴속도 등 수치적 성능을 기준으로 실제 비근사최적화 결과와 비교검토 되었다.