• Proceedings of the KIEE Conference
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• 1996.07b
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• pp.734-736
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• 1996

This paper presents a method of calculating a selective number of eigenvalues in power systems, which are rightmost, or are largest modulus. The modified Arnoldi method in conjunction with implicit shift OR-algorithm is used to calculate the rightmost eigenvalues. Algorithm requires neither a prior knowledge of the specified shifts nor the calculation of inverse matrix. The key advantage of the algorithm is its ability to converge to the wanted eigenvalues at once. The method is compared with the modified Arnoldi method combined with S-matrix transformation, where the eigenvalues having the largest modulus are to be determined. The two methods are applied to the reduced Kansai system. Convergence characteristics and performances are compared. Results show that both methods are robust and has good convergence properties. However, the implicit shift OR method is seen to be faster than the S-matrix method under the same condition.

• Advances in aircraft and spacecraft science
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• v.3 no.1
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• pp.45-59
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• 2016

In this paper, the condensation method which is based on the Rayleigh-Ritz method, is described for the free vibration analysis of axially loaded slightly curved beams subject to partial axial restraints. If the longitudinal inertia is neglected, some of the Rayleigh-Ritz minimization equations are independent of the frequency. These equations can be used to formulate a relationship between the weighting coefficients associated with the lateral and longitudinal displacements, which leads to "connection coefficient matrix". Once this matrix is formed, it is then substituted into the remaining Rayleigh-Ritz equations to obtain an eigenvalue equation with a reduced matrix size. This method has been applied to simply supported and partially clamped beams with three different shapes of imperfection. The results indicate that for small imperfections resembling the fundamental vibration mode, the sum of the square of the fundamental natural and a non-dimensional axial load ratio normalized with respect to the fundamental critical load is approximately proportional to the square of the central displacement.

• Journal of the Korean Society for Precision Engineering
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• v.16 no.5 s.98
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• pp.200-208
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• 1999

The statics relation of the Stewart platform has been investigated from the viewpoint of the forward and inverse force transmission analyses. Two eigenvalue problems corresponding to the forward and inverse force transmission analyses have been formulated. The forward force transmission analysis is to determine the ranges of the magnitudes of the force and moment generated at the end-effector for the given magnitude of linear actuator forces. In reverse order, the inverse force transmission analysis is to find the range of the magnitude of actuator forces for the given ranges of the magnitudes of the force and moment at the end-effector. The inverse force transmission analysis is important since it can provide a designer with a valuable information about how to choose the linear actuators. It has been proved that two eigenvalue problems have a reciprocal relation, which implies that solving either of the eigenvalue problems may complete the forward/inverse force transmission analysis. A numerical example has been also presented.

• 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 KIPS Transactions:PartA
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• v.11A no.1
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• pp.67-74
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• 2004

Most of today's parallel numerical schemes use synchronous algorithms, where some processors that have finished their tasks earlier than others must wait at synchronization points for correct computation. Hence overall performance of the system is dependent upon the speed of the slowest processor. In this paper, we det·ise a synchronous/asynchronous hybrid algorithm to accelerate convergence of the solution for finding the dominant eigenpair of a large matrix, by reducing the idle times of faster processors using MPMD programming methodology.

• Coupled systems mechanics
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• v.2 no.4
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• pp.349-374
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• 2013

In this work we propose a novel procedure for direct computation of buckling loads for extreme mechanical or thermomechanical conditions. The procedure efficiency is built upon the von Karmann strain measure providing the special format of the tangent stiffness matrix, leading to a general linear eigenvalue problem for critical load multiplier estimates. The proposal is illustrated on a number of validation examples, along with more complex examples of interest for practical applications. The comparison is also made against a more complex computational procedure based upon the finite strain elasticity, as well as against a more refined model using the frame elements. All these results confirm a very satisfying performance of the proposed methodology.

• The Transactions of the Korean Institute of Electrical Engineers C
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• v.48 no.2
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• pp.141-146
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• 1999

The eigenvalue equations of multiple waveguides with step-index profile are derived by using the WKB theory. Phase changes unique to step-index discontinuity areintroduced when applying the WKB connection formula to turning points. The transfer matrix method is employed for the analysis of multiple structure and the derived eigenvalue equation are represented in the recursive form. The results by the WKB are compared with those by the FEM for a three-waveguide coupler.

• The Journal of the Acoustical Society of Korea
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• v.20 no.4E
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• pp.39-44
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• 2001

We investigate the numerical instability of linear prediction for discrete harmonic spectra of audio signals. It is identified that the eigenvalue spread is very large when discrete harmonic spectra are confined only in a lower part of the entire signal bandwidth. A simple method that redefines the sampling frequency and associate harmonic frequencies is proposed to improve the numerical stability. Simulation results using real audio signals indicate its superior stabilizing ability and improved accuracy in the discrete spectral estimation for both LP and DAP.

• Steel and Composite Structures
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• v.21 no.4
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• pp.791-803
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• 2016

In this article, the problem of a two-dimensional thermoelastic half-space are studied using mathematical methods under the purview of the generalized thermoelastic theory with one relaxation time is studied. The surface of the half-space is taken to be thermally insulated and traction free. Accordingly, the variations of physical quantities due to by laser pulse given by the heat input. The nonhomogeneous governing equations have been written in the form of a vector-matrix differential equation, which is then solved by the eigenvalue approach. The analytical solutions are obtained for the temperature, the components of displacement and stresses. The resulting quantities are depicted graphically for different values of thermal relaxation time. The result provides a motivation to investigate the effect of the thermal relaxation time on the physical quantities.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.6 no.9
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• pp.1998-2016
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• 2012

Reliable spectrum sensing algorithm is a fundamental component in cognitive radio. In this paper, a non-cooperative spectrum sensing algorithm which needs only one cognitive radio node named CORDIC (Coordinate Rotation Digital Computer) Jacobi based method is proposed. The algorithm computes the eigenvalues of the sampled covariance of received signal mainly by shift and additional operations, which is suitable for hardware implementation. Based the latest random matrix theory (RMT) about the distribution of the limiting maximum and minimum eigenvalue ratio, the relationship between the probability of false alarm and the decision threshold is derived. Simulations and discussions show the method is effective. Real captured digital television (DTV) signals and Universal Software Radio Peripheral (USRP) are also employed to evaluate the performance of the algorithm, which prove the proposed algorithm can be applied in practical spectrum sensing applications.