• Journal of the Korean Statistical Society
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• v.22 no.2
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• pp.339-345
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• 1993

It is well known that distribution of functions of eigen values and vectors of a certain matrix plays an important role in multivariate analysis. This paper deals with the transformation of a correlation-type random matrix to its eigen values and vectors. Properties of the transformation are also considered. The results obtained are applied to express the joint distribution of eigen values and vectors of the correlation matrix when sample is taken from a m-variate spherical distribution.

• Journal of the Institute of Electronics and Information Engineers
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• v.50 no.11
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• pp.28-35
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• 2013

The Krylov-Schur algorithm has been applied to reveal the eigen-properties of the wave guide having the square cross section. The eigen-matrix equation has been constructed from FEM with the basis function of the tangential edge-vectors of the triangular element. This equation has been treated firstly with Arnoldi decomposition to obtain a upper Hessenberg matrix. The QR algorithm has been carried out to transform it into Schur form. The several eigen values satisfying the convergent condition have appeared in the diagonal components. The eigen-modes for them have been calculated from the inverse iteration method. The wanted eigen-pairs have been reordered in the leading principle sub-matrix of the Schur matrix. This sub-matrix has been deflated from the eigen-matrix equation for the subsequent search of other eigen-pairs. These processes have been conducted several times repeatedly. As a result, a few primary eigen-pairs of TE and TM modes have been obtained with sufficient reliability.

• The Korean Journal of Applied Statistics
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• v.17 no.1
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• pp.119-134
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• 2004

Generally to estimate the priority vector in AHP, an eigen-vector method or a log-arithmic least square method is applied to pairwise comparison matrix itself. In this paper an estimating method is suggested, which is applied to pairwise comparison matrix adjusted by using the eigen-decomposition of skew-symmetric matrix. We also show theoretical background, meanings, and several advantages of this method by example. This method may be useful in case that pairwise comparison matrix is quite inconsistent.

• The Journal of Information Technology and Database
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• v.6 no.2
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• pp.19-28
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• 1999

Digital image and video libraries require new algorithms for the automated extraction and indexing of salient image features. Eigen values of an image provide one important cue for the discrimination of image content. In this paper we propose a new approach for automated content extraction that allows efficient database searching using eigen values. The algorithm automatically extracts eigen values from the image matrix represented by the covariance matrix for the image. We demonstrate that the eigen values representing shape information and the skewness of its distribution representing complexity provide good performance in image query response time while providing effective discriminability. We present the eigen value extraction and indexing techniques. We test the proposed algorithm of searching by eigen value and its skewness on a database of 100 images.

• The Transactions of the Korea Information Processing Society
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• v.5 no.1
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• pp.97-102
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• 1998

In the most cases of eigen value problems in the social sciences, the object matrix to analyze is real-valued symmetric matrix. And many cases of eigen value problems in this field needs 2-4 eigen pairs according to the magnitude of their absolute values. The methods to obtain eigen pairs by numerical computation using computer, we would face the problem of round off error because matrix computation needs a number of calculations. In this paper, an algorithm which make us to get some needed eigcn pairs according to the magnitude of their absolute values is designed. And in this algorithm, the power method is used to obtain some eigen pairs. This algorithm is expected to be effective by the reduction of the number of calculations.

• Proceedings of the KSRS Conference
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• 2003.11a
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• pp.316-318
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• 2003

An eigen-analysis of the coherency matrix provides the polarimetric scattering mechanisms with the matrix characterizing parameters. In this paper, the coherency matrices of deciduous and coniferous vegetation are calculated using the analytical method. The Generalized Rayleigh-Gans approximation is used to model backscattering from distributed coniferous and deciduous leaves. The characteristics of eigen-parameters of simulated coherency matrix for deciduous and coniferous leaves with respect to the leaf shapes and orientations are illustrated.

• Proceedings of the KIEE Conference
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• 1996.07b
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• pp.749-753
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• 1996

This paper presents a new method for first and second order eigen-sensitivity analysis of system matrix in augmented form. Eigen-sensitivity analysis provides invaluable informations in power system planning and operation. However, conventional eigen-sensitivity analysis methods, which need all the eigenvalues and eigenvectors, can not be applicable to large scale power systems due to large computer memory and computing time required. In the proposed method, all sensitivity computations for a mode are carried out using the augmented system matrix and its own eigenvalue and right & left eigenvectors. In other words sensitivity analysis for a mode does not need informations on the other eigenvalues and eigenvectors and sparsity technique can be fully utilized. Thus compuations can be done very efficiently with moderate computer memory and computing time even for large power systems. The proposed algorithm is tested for one machine infinite bus system.

• Kyungpook Mathematical Journal
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• v.57 no.2
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• pp.211-222
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• 2017

In this paper, we consider three inverse eigenvalue problems for a special type of acyclic matrices. The acyclic matrices considered in this paper are described by a graph called a broom on n + m vertices, which is obtained by joining m pendant edges to one of the terminal vertices of a path on n vertices. The problems require the reconstruction of such a matrix from given partial eigen data. The eigen data for the first problem consists of the largest eigenvalue of each of the leading principal submatrices of the required matrix, while for the second problem it consists of an eigenvalue of each of its trailing principal submatrices. The third problem has an eigenvalue and a corresponding eigenvector of the required matrix as the eigen data. The method of solution involves the use of recurrence relations among the leading/trailing principal minors of ${\lambda}I-A$, where A is the required matrix. We derive the necessary and sufficient conditions for the solutions of these problems. The constructive nature of the proofs also provides the algorithms for computing the required entries of the matrix. We also provide some numerical examples to show the applicability of our results.

• Transactions of the Korean Society of Mechanical Engineers
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• v.15 no.2
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• pp.445-454
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• 1991

In this thesis, Mindlin plate element with nine nodes and three degrees-of-freedom at each node is formulated and is employed in eigen-analysis of a rectangular plates in order to alleviate locking phenomenon of eigenvalues. Eigenvalues and their modes may be locked if conventional $C_{0}$-isoparametric element is used. In order to reduce stiffness locking phenomenon, two methods (1, the general reduced and selective integration, 2, the new element that use of modified shape function) are studied. Additionally in order to reduce the error due to mass matrix, two mass matrixes (1, Gauss-Legendre mass matrix, 2, Gauss-Lobatto mass matrix) are considered. The results of eigen-analysis for two models (the square plate with all edges simply-supported and all edges built-in), computed by two methods for stiffness matrix and by two mass matrixes are compared with theoretical solutions and conventional numerical solutions. These comparisons show that the performance of the two methods with Gauss-Lobatto mass matrix is better than that of the conventional plate element. But, by considering the spurious rigid body motions, the element which employs modified shape function with full integration and Gauss-Lobatto mass matrix can elevate the accuracy and convergence of numerical solutions.

• Proceeding of EDISON Challenge
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• 2016.03a
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• pp.195-202
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• 2016

In this paper, crack detection method using eigen value analysis is presented. Three methods are used: theoretical analysis, finite element method with the cracked beam elements and finite element method with three dimensional continuum elements. Finite element formulation of the cracked beam element is introduced. Additional term about stress intensity factor based on fracture mechanics theory is added to flexibility matrix of original beam to model the crack. As using calculated stiffness matrix of cracked beam element and mass matrix, natural frequencies are calculated by eigen value analysis. In the case of using continuum elements, the natural frequencies could be calculated by using EDISON CASAD solver. Several cases of crack are simulated to obtain natural frequencies corresponding the crack. The surface of natural frequency is plotted as changing with crack location and depth. Inverse analysis method is used to find crack location and depth from the natural frequencies of experimental data, which are referred by another papers. Predicted results are similar with the true crack location and depth.