• The Journal of Natural Sciences
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• v.9 no.1
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• pp.69-74
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• 1997

We introduce the Crawford number and codal metric to analyze perturbation bounds of the generalized eigenvalue problem.

• Journal of the Korean Institute of Telematics and Electronics
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• v.23 no.4
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• pp.455-459
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• 1986

A large set of linear equations which arise in many applications, such as in digital signal processing, image filtering, estimation theory, numerical analysis, etc. involve the problem of a tridiagonal matrix. In this paper, the determinant, eigenvalue and inverse matrix of a tridiagoanl matrix are analytically evaluated.

• Journal of applied mathematics & informatics
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• v.40 no.5_6
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• pp.949-958
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• 2022

The aim of this papaer is to prove the discrete compactness property for modified Raviart-Thomas element(MRT) of lowest order on quadrilateral meshes. Then MRT space can be used for eigenvalue problems, and is more efficient than the lowest order ABF space since it has less degrees of freedom.

• Proceedings of the Korean Nuclear Society Conference
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• 1997.05a
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• pp.27-32
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• 1997

In this paper, a new multigrid method is developed to solve the reactor eigenvalue problems. The new algorithm can be used in any matrix equation concerned with the eigenvalue problem. The finite difference neutron diffusion problem is considered demonstration of the performance of the new multigrid algorithm. The numerical results show that the new multigrid algorithm works well and requires much shorter (7~10 times) computing time compaired to the production code VENTURE.

• 제어로봇시스템학회:학술대회논문집
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• 1996.10b
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• pp.253-256
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• 1996

In this paper, A new time-varying sliding surface design using eigenvalue locus is proposed to achieve fast and robust in a class of high-order uncertain dynamic system. A moving sliding surface(MSS) was proposed earlier for the second-order variable structure control systems(VSCS). This methodology led to fast and robust control responses of the second-order VSCS. However, the moving algorithm of the MSS was too complicated to be employed the high-order VSCS. To resolve this problem, we propose a new moving algorithm that switching surface moves such that the eigenvalues of equivalent system in the sliding mode have a predetermined locus. Using the proposed surface fast and robust behaviors are accomplished. The problem of chattering can be eliminated by using a boundary layer of switching surface. The efficiency of proposed algorithm is illustrated by an application to four-order workbench.

• Structural Engineering and Mechanics
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• v.4 no.3
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• pp.277-301
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• 1996

A finite element model of a beam element with flexible connections is used to investigate the effect of the randomness in the stiffness values on the modal properties of the structural system. The linear behavior of the connections is described by a set of random fixity factors. The element mass and stiffness matrices are function of these random parameters. The associated eigenvalue problem leads to eigenvalues and eigenvectors which are also random variables. A second order perturbation technique is used for the solution of this random eigenproblem. Closed form expressions for the 1st and 2nd order derivatives of the element matrices with respect to the fixity factors are presented. The mean and the variance of the eigenvalues and vibration modes are obtained in terms of these derivatives. Two numerical examples are presented and the results are validated with those obtained by a Monte-Carlo simulation. It is found that an almost linear statistical relation exists between the eigenproperties and the stiffness of the connections.

• Journal of KSNVE
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• v.8 no.3
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• pp.408-419
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• 1998

Dynamic characteristics are investigated when a nonlinear system showing periodic and chaotic responses under harmonic excitation is exposed to random perturbation. Approach for both qulitative and quantitative analysis of the noise effect in a nonlinear system under harmonic excitation is presented. For the qualitative analysis, Lyapunov exponents are calculated and Poincar map is illustrated. For the quatitative analysis. Fokker-Planck equatin is solved numerical by means of a Path-integral solution procedure. Eigenvalue problem obtained from the numerical caculation is solved and the relation of eigenvalue, eigenvector and chaotic motion is investigated.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1998.10a
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• pp.431-438
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• 1998

An efficient solution method is presented to solve the eigenvalue problem arising in tile dynamic analysis of non-proportionally damped structural systems with multiple or close eigenvalues. The proposed method is obtained by applying the modified Newton-Raphson technique and the orthonormal condition of the eigenvectors to the quadratic eigenvalue problem. Even if the shift value is an eigenvalue of the system, the proposed method guarantees nonsingularity, which is analytically proved. The initial values of the proposed method can be taken as the intermediate results of iteration methods or results of approximate methods. Two numerical examples are also 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.

• Journal of Mechanical Science and Technology
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• v.20 no.1
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• pp.158-166
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• 2006

Extended Graetz problem in microtube is analyzed by using eigenfunction expansion to solve the energy equation. For the eigenvalue problem we applied the shooting method and Galerkin method. The hydrodynamically isothermal developed flow is assumed to enter the microtube with uniform temperature or uniform heat flux boundary condition. The effects of velocity and temperature jump boundary condition on the microtube wall, axial conduction and viscous dissipation are included. From the temperature field obtained, the local Nusselt number distributions on the tube wall are obtained as the dimensionless parameters (Peclet number, Knudsen number, Brinkman number) vary. The fully developed Nusselt number for each boundary condition is obtained also in terms of these parameters.

• Journal of the Korean Institute of Intelligent Systems
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• v.10 no.2
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• pp.161-167
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• 2000

In this paper, we propose a design method for BAMs(bidirectiona1 associative memories) which can perform the function of bidirectional association efficiently. Based on the theoretical investigation about the properties of BAMs, we first formulate the problem of finding a BAM that can store the given pattern pairs as stable states with high error correction ratio in the form of a constrained optimization problem. Next, we transform the constrained optimization problem into a GEVP(genera1ized eigenvalue problem), which can be solved by recently developed interior point methods. The applicability of the proposed method is illustrated via design examples.