• Journal for History of Mathematics
• /
• v.17 no.4
• /
• pp.133-152
• /
• 2004

In this paper, we discuss students' conceptual development of eigen value and eigen vector in differential equation course based on reformed differential equation using the mathematical model of mass spring according to historico-generic principle. Moreover, in setting of small group interactive learning, we investigate the students' development of mathematical attitude.

• Journal of the Computational Structural Engineering Institute of Korea
• /
• v.20 no.6
• /
• pp.691-697
• /
• 2007

Numerical eigen analysis of beam-like structure can be easily and effectively done by various conventional beam theory-based methods. However, in case of the structures composed of composite-sectioned beams, the application of conventional numerical methods requires one to derive both equivalent material and geometry properties. In the present paper, these equivalent properties are derived by the transformed section method and the test FEM program is coded. The numerical accuracy of the proposed method is verified through the comparison with the ANSYS 3-D model.

• Proceedings of the Computational Structural Engineering Institute Conference
• /
• 2011.04a
• /
• pp.587-588
• /
• 2011

본 논문에서는 강사장교의 극한강도 및 파괴모드를 간략하게 예측할 수 있는 간단하고 빠른 해석법을 제안하였다. 기존의 비탄성 고유치해석의 기본 개념을 바탕으로 기둥 요소에 대한 수렴 기준을 보였고, 사장교 구조 시스템의 거더 및 주탑 요소에서 보-기둥 거동을 고려하기 위한 새로운 수렴 기준을 제시하였다. 제시된 방법의 타당성 검증을 위하여 중앙경간 길이와 거더의 높이를 변화시킨 강사장교 모델에 대하여 제안된 비탄성 고유치 해석과 비선형 탄소성 해석 결과를 비교하였다. 해석 결과, 제안된 수렴 기준을 적용한 비탄성 고유치 해석은 기존에 기둥의 수렴기준을 적용했던 방법에 비하여 강사장교의 극한강도를 보다 정확히 예측할 수 있었다. 또한, 제안된 방법은 강사장교의 파괴모드 역시 근사하게 모사 가능함을 알 수 있었다.

• Journal of the Earthquake Engineering Society of Korea
• /
• v.2 no.1
• /
• pp.71-78
• /
• 1998

The eigenvalue problem is presented for the building with added viscoelastic dampers by using component mode method. The Lagrange multiplier formulation is used to derive the eigenvalue problem which is expressed with the natural frequencies of the building, the mode components at which the dampers are added, and the viscoelastic property of the damper. The derived eigenvalue problem has a nonstandard form for determining the eigenvalues. Therefore, the problem is examined by the graphical depiction to give new insight into the eigenvalues for the building with added viscoelastic dampers. Using the present approach the exact eigenvalues can be found and also upper and lower bounds of the eigenvalues can be obtained.

• Proceedings of the Earthquake Engineering Society of Korea Conference
• /
• 2002.09a
• /
• pp.364-370
• /
• 2002

본 논문에서는 양자물리학 분야에서 Lanczos 방법의 수렴을 가속화하기 위해 개발된 바 있는 행렬의 거듭제곱 기법을 동역학 분야의 Lanczos 순환식에 도입함으로써 구조물의 고유치 해석의 효율성을 향상시켰다 행렬의 거듭제곱 기법을 도입한 Lanczos 방법이 기존의 방법보다 수렴성이 더욱 우수하다. 수치예제를 통해 행렬의 거듭제곱 기법을 도입한 Lanczos 방법의 효율성을 검증하였으며 제안방법을 통한 고유치 해석에 있어서 가장 적합한 거듭제곱값을 제시하였다.

• The Korean Journal of Applied Statistics
• /
• v.7 no.1
• /
• pp.69-74
• /
• 1994

Kim (1992) derived influence functions of rows and columns on the eigenvalues obtained in correspondence analysis (CA) of two-way contingency tables. As in principal component analysis, the eigenvalues are of great importance in CA. The goodness of a two dimensional correspondence plot is determined by the ratio of the sum of the two largest eigenvalues to the sum of all the eigenvalues. By investigating those rows and columns with high influence, a correspondence plot may be improved. In this paper, we extend the influence functions of CA to multiple correspondence analysis (MCA), which is a CA of multi-way contigency tables. An explicit formula of the influence function is given.

• Computational Structural Engineering
• /
• v.11 no.1
• /
• pp.205-216
• /
• 1998

A solution method is presented to solve the eigenvalue problem arising in the dynamic analysis of nonclassicary damped structural systems with multiple eigenvalues. The proposed method is obtained by applying the modified Newton-Raphson technique and the orthonormal condition of the eigenvectors to the linear eigenproblem through matrix augmentation of the quadratic eigenvalue problem. In the iteration methods such as the inverse iteration method and the subspace iteration method, singularity may be occurred during the factorizing process when the shift value is close to an eigenvalue of the system. However, even though the shift value is an eigenvalue of the system, the proposed method provides nonsingularity, and that is analytically proved. Since the modified Newton-Raphson technique is adopted to the proposed method, initial values are need. Because the Lanczos method effectively produces better initial values than other methods, the results of the Lanczos method are taken as the initial values of the proposed method. Two numerical examples are presented to demonstrate the effectiveness of the proposed method and the results are compared with those of the well-known subspace iteration method and the Lanczos method.

• The Journal of the Acoustical Society of Korea
• /
• v.32 no.6
• /
• pp.548-555
• /
• 2013

The localization of sources has a numerous number of applications. To estimate the position of sources, the relative delay between two or more received signals for the direct signal must be determined. Although the generalized cross-correlation method is the most popular technique, an approach based on eigenvalue decomposition (EVD) is also popular one, which utilizes an eigenvector of the minimum eigenvalue. The performance of the eigenvalue decomposition (EVD) based method degrades in the low SNR and the correlated environments, because it is difficult to select a single eigenvector for the minimum eigenvalue. In this paper, we propose a new adaptive algorithm based on Canonical Correlation Analysis (CCA) in order to extend the operation range to the lower SNR and the correlation environments. The proposed algorithm uses the eigenvector corresponding to the maximum eigenvalue in the generalized eigenvalue decomposition (GEVD). The estimated eigenvector contains all the information that we need for time delay estimation. We have performed simulations with uncorrelated and correlated noise for several SNRs, showing that the CCA based algorithm can estimate the time delays more accurately than the adaptive EVD algorithm.

• Investigative Magnetic Resonance Imaging
• /
• v.11 no.2
• /
• pp.110-118
• /
• 2007

Purpose: The objective of this work to construct eigenvalue maps that have information of magnitude of three primary diffusion directions using diffusion tensor images. Materials and Methods: To construct eigenvalue maps, we used a 3.0T MRI scanner. We also compared the Moore-Penrose pseudo-inverse matrix method and the SVD (single value decomposition) method to calculate magnitude of three primary diffusion directions. Eigenvalue maps were constructed by calculating of magnitude of three primary diffusion directions. We did investigate the relationship between eigenvalue maps and fractional anisotropy map. Results: Using Diffusion Tensor Images by diffusion tensor imaging sequence, we did construct eigenvalue maps of three primary diffusion directions. Comparison between eigenvalue maps and Fractional Anisotropy map shows what is difference of Fractional Anisotropy value in brain anatomy. Furthermore, through the simulation of variable eigenvalues, we confirmed changes of Fractional Anisotropy values by variable eigenvalues. And Fractional anisotropy was not determined by magnitude of each primary diffusion direction, but it was determined by combination of each primary diffusion direction. Conclusion: By construction of eigenvalue maps, we can confirm what is the reason of fractional anisotropy variation by measurement the magnitude of three primary diffusion directions on lesion of brain white matter, using eigenvalue maps and fractional anisotropy map.

• Computational Structural Engineering
• /
• v.10 no.3
• /
• pp.185-193
• /
• 1997

The order of the stress singularity that occurs at the termination of an interface between materials exhibiting bilinear stress-strain response under plane strain conditions has been calculated, The governing equation of elasticity together with traction-free boundary condition and interface continuity condition defines a two-point boundary value problem. The stress components near the free edge are assumed to be proportional to r/sup s-1/, with solutions existing only for certain values of s. Finding these values entails the solution of an eigenvalue problem. Because it has been impossible to integrate the differential equations analytically, the integration has been performed numerically with a shooting method coupled with a Newton improvement scheme.