• Journal of Institute of Control, Robotics and Systems
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• v.18 no.10
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• pp.895-901
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• 2012

The stability robustness problem of linear discrete systems with time-varying unstructured uncertainty of delayed states with time-varying delay time is considered. The proposed conditions for stability can be used for finding allowable bounds of timevarying uncertainty and delay time, which are solved by using LMI (Linear Matrix Inequality) and GEVP (Generalized Eigenvalue Problem) known as powerful computational methods. Furthermore, the conditions can imply the several previous results on the uncertainty bounds of time-invariant delayed states. Numerical examples are given to show the effectiveness of the proposed algorithms.

• Journal of applied mathematics & informatics
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• v.22 no.1_2
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• pp.467-474
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• 2006

We present and study the stability and convergence of a deflation-preconditioned conjugate gradient(PCG) scheme for the interior generalized eigenvalue problem $Ax = {\lambda}Bx$, where A and B are large sparse symmetric positive definite matrices. Numerical experiments are also presented to support our theoretical results.

• Interaction and multiscale mechanics
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• v.1 no.2
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• pp.211-230
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• 2008

Owing to the growing size of the eigenvalue problem and the growing number of eigenvalues desired, solution methods of iterative nature are becoming more popular than ever, which however suffer from low efficiency and lack of proper convergence criteria. In this paper, three efficient iterative eigenvalue algorithms are considered, i.e., subspace iteration method, iterative Ritz vector method and iterative Lanczos method based on the cell sparse fast solver and loop-unrolling. They are examined under the mode error criterion, i.e., the ratio of the out-of-balance nodal forces and the maximum elastic nodal point forces. Averagely speaking, the iterative Ritz vector method is the most efficient one among the three. Based on the mode error convergence criteria, the eigenvalue solvers are shown to be more stable than those based on eigenvalues only. Compared with ANSYS's subspace iteration and block Lanczos approaches, the subspace iteration presented here appears to be more efficient, while the Lanczos approach has roughly equal efficiency. The methods proposed are robust and efficient. Large size tests show that the improvement in terms of CPU time and storage is tremendous. Also reported is an aggressive shifting technique for the subspace iteration method, based on the mode error convergence criteria. A backward technique is introduced when the shift is not located in the right region. The efficiency of such a technique was demonstrated in the numerical tests.

• Honam Mathematical Journal
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• v.45 no.3
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• pp.457-470
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• 2023

In this study, we set a boundary value problem (BVP) consisting of a discrete Sturm-Liouville equation with transmission condition and boundary conditions depending on generalized eigenvalue parameter. Discussing the Jost and scattering solutions of this BVP, we present scattering function and find some properties of this function. Furthermore, we obtain resolvent operator, continuous and discrete spectrum of this problem and we give an valuable asymptotic equation to get the properties of eigenvalues. Finally, we give an example to compare our results with other studies.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.5 no.2
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• pp.63-69
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• 2001

In this study, we shall be concerned with computing in parallel a few of the smallest eigenvalues and their corresponding eigenvectors of the eigenvalue problem, $Ax={\lambda}Bx$, where A is symmetric, and B is symmetric positive definite. Both A and B are large and sparse. Recently iterative algorithms based on the optimization of the Rayleigh quotient have been developed, and CG scheme for the optimization of the Rayleigh quotient has been proven a very attractive and promising technique for large sparse eigenproblems for small extreme eigenvalues. As in the case of a system of linear equations, successful application of the CG scheme to eigenproblems depends also upon the preconditioning techniques. A proper choice of the preconditioner significantly improves the convergence of the CG scheme. The idea underlying the present work is a parallel computation of the Multi-Color Block SSOR preconditioning for the CG optimization of the Rayleigh quotient together with deflation techniques. Multi-Coloring is a simple technique to obatin the parallelism of order n, where n is the dimension of the matrix. Block SSOR is a symmetric preconditioner which is expected to minimize the interprocessor communication due to the blocking. We implemented the results on the CRAY-T3E with 128 nodes. The MPI(Message Passing Interface) library was adopted for the interprocessor communications. The test problems were drawn from the discretizations of partial differential equations by finite difference methods.

• The Journal of the Acoustical Society of Korea
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• v.25 no.2E
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• pp.43-48
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• 2006

Abstract-Using the recursive generalized eigendecomposition method, we develop a recursive form solution to the data least squares (DLS) problem, in which the error is assumed to lie in the data matrix only. Simulations demonstrate that DLS outperforms ordinary least square for certain types of deconvolution problems.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2005.11b
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• pp.49-52
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• 2005

Flutter analysis procedure can be divided into two steps such as the computation of generalized mass, stiffness, and unsteady aerodynamic matrices and the calculation of major vibration modes frequency and damping values at each flight speed by solving the complex eigenvalue problem. In aircraft flutter analyses, most of the time is spent in the process of computing the unsteady aerodynamic matrices at each Mach-reduced frequency pairs defined. In this study, the method has been presented for computation and extraction of unsteady aerodynamic matrix portions dependent only on aerodynamic model using DMAP ALTER in MSC/NASTRAN SOL 145. In addition, efficient flutter analysis method has been suggested by computing and utilizing the unsteady generalized aerodynamic matrices for each analysis condition using the unsteady aerodynamic matrix portions extracted above.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.3 no.1
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• pp.99-106
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• 1999

An accelerated optimization technique combined with a stepwise deflation procedure is presented for the efficient evaluation of a few of the smallest eigenvalues and their corresponding eigenvectors of the generalized eigenproblems. The optimization is performed on the Rayleigh quotient of the deflated matrices by the aid of a preconditioned conjugate gradient scheme with the incomplete Cholesky factorization.

• Proceedings of the KIEE Conference
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• 2003.11c
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• pp.588-591
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• 2003

This paper presents a new short-term load forecasting system using data mining. Since the electric load has very different pattern according to the day, it definitely gives rise to the forecasting error if only one forecasting model is used. Thus, to resolve this problem, the fuzzy model-based classifier and predictor are proposed for the forecasting of the hourly electric load. The proposed classifier is the multi-input and multi-output fuzzy system of which the consequent part is composed of the Bayesian classifier. The proposed classifier attempts to categorize the input electric load into Monday, Tuesday$\sim$Friday, Saturday, and Sunday electric load, Then, we construct the Takagi-Sugeno (T-S) fuzzy model-based predictor for each class. The parameter identification problem is converted into the generalized eigenvalue problem (GEVP) by formulating the linear matrix inequalities (LMIs). Finally, to show the feasibility of the proposed method, this paper provides the short-term load forecasting example.

• 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.