• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.3 no.2
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• pp.37-49
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• 1999

In this paper we develop a general Homotopy method called the Group Homotopy method to solve the symmetric eigenproblem. The Group Homotopy method overcomes notable drawbacks of the existing Homotopy method, namely, (i) the possibility of breakdown or having a slow rate of convergence in the presence of clustering of the eigenvalues and (ii) the absence of any definite criterion to choose a step size that guarantees the convergence of the method. On the other hand, We also have a good approximations of the largest eigenvalue of a Symmetric matrix from Lanczos algorithm. We apply it for the largest eigenproblem of a very large symmetric matrix with a good initial points.

• Journal of the Korean Operations Research and Management Science Society
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• v.26 no.4
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• pp.71-82
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• 2001

Using the computer simulation method, we invest19ate the probability distribution of maximum eigenvalue of pair-wise comparison matrix, which has been used as a parameter for measuring the consistency of responses in analytic hierarchy process (AHP). We show that the shape of the distribution of the maximum eigenvalue is different according to the dimension of the matrix. In addition, we cannot find any evidence that the distribution of the Consistency Index is a Normal distribution, which has been claimed in the Previous literature. Accordingly, we suggest using so called K-index calcu1ated based on the concept of cumulative distribution function lather than based on that of arithmetic mean because the probabilistic distribution cannot be assumed to be a Normal distribution. We interpret the simulation results by comparing them with the suggestion of Saaty[11]. Our results show that using Saaty＇s value could be too generous when the dimension of the matrix is 3 and strict over 4. Finally, we propose new criteria for measuring the response consistency in AHP.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.24 no.6A
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• pp.888-893
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• 1999

This paper introduces M-ary multitrack run-length (d.k) constrained codes for optical storage systems. We calculate capacities and densities of the codes. We have driven a general form of the state transition matrix for M-ary multitrack (d,k) codes. Using the largest eigenvalue of the transition matrix, we calculate the capacity and density. The capacity approaches to the limit with a small k constraint compared to single-track codes.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.17 no.1 s.118
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• pp.80-87
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• 2007

In this paper, a method for identifying the location and extent of a damage in a structure using residual forces was presented. Element stiffness matrix reduction parameters in a finite element model were used to describe the damaged structure mathematically. The element stiffness matrix reduction parameters were determined by minimizing a global error derived from dynamic residual vectors, which were obtained by introducing a simulated experimental data into the eigenvalue problem. Genetic algorithm was used to get the solution set of element stiffness reduction parameters. The proposed scheme was verified using Euler-Bernoulli beam. The results were presented in the form of tables and charts.

• Structural Engineering and Mechanics
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• v.38 no.2
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• pp.195-210
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• 2011

Bernoulli-Euler beam theory is used to develop an exact dynamic stiffness matrix for the flexural-torsional coupled motion of a three-dimensional, axially loaded, thin-walled beam of doubly asymmetric cross-section. This is achieved through solution of the differential equations governing the motion of the beam including warping stiffness. The uniform distribution of mass in the member is also accounted for exactly, thus necessitating the solution of a transcendental eigenvalue problem. This is accomplished using the Wittrick-Williams algorithm. Finally, examples are given to confirm the accuracy of the theory presented, together with an assessment of the effects of axial load and loading eccentricity.

• Communications of the Korean Mathematical Society
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• v.7 no.1
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• pp.123-128
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• 1992

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.4 no.1
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• pp.79-92
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• 2000

We investigate numerical properties of Newton's algorithm for improving an eigenpair of a real matrix A using only fixed precision arithmetic. We show that under natural assumptions it produces an eigenpair of a componentwise small relative perturbation of the data matrix A.

• The Journal of Fisheries Business Administration
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• v.15 no.1
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• pp.58-80
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• 1984

The classification of islands is prerequisite for establishing a development policy to vitalize many-sided function of islands. We try to classify the 440 inhabited islands which exist in Jeon-Nam area and Kyong-Nam area by means of PCA. PCA begins with making correlation matrix of orignal variables. From this matrix we can comprehend the rough relationships between two variables. Next, we look for the eigenvalues which are roots of characteristic equation of correlation matrix. The number of eigenvalues is equal to that of original variables. We choose the largest eigenvalue λ$_1$among them and then look for the eigenvector of correlation matrix corresponding to the largest eigenvalue. Linear combination of eigenvector obtained above and original variables is namely first Principal Component (PC). Using an eigenvalue criterion(λ$\geq$ 1), we choose 3 PCs in Jeon-Nam area and 2 PCs in Kyong-Nam area. But we decide to consider only two PCs in both areas to faciliate a comparative analysis. Now, loss of information is 31.7% in Jeon-Nam area and 26.64% in Kyong-Nam area. PCs extracted by preceding procedure have characteristics as follows. The first PC relates to aggregate size of islands in case of both areas. The second PC relates to income per household, factors of agricultural production and factors of fisheries production in Jeon-Nam area, but in Kyong-Nam area it means distance from island and income per household. A classification of islands can be attained by plotting component scores of each island in graph used two PCs as axes and grouping similiar islands. 6 groups are formed in Jeon-Nam area and 5 groups in Kyong-Nam area. The result of this study in kyong-Nam area accords with prior result of study.

• Communications for Statistical Applications and Methods
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• v.12 no.3
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• pp.653-657
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• 2005

Eigenstructure of a spatial design matrix of Matheron's variogram estimator in $R^1$ is derived. It is shown that the spatial design matrix in $R^1$ with n/2$\le$h < n has a nice spectral decomposition. The mean, variance, and covariance of this estimator are obtained using the eigenvalues of a spatial design matrix. We also found that the lower bound and the upper bound of the normalized Matheron's variogram estimator.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2002.04a
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• pp.133-140
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• 2002

This paper investigates the applicability of the modified Lanczos method using the power technique, which was developed in the field of quantum physics, to the eigenproblem in the field of engineering mechanics by introducing matrix-powered Lanczos recursion and numerically evaluating the suitable power value. The matrix-powered Lanczos method has better convergence and less operation count than the conventional Lanczos method. By analyzing four numerical examples, the effectiveness of the matrix-powered Lanczos method is verified and the appropriate matrix power is also recommended.