• The Journal of Korean Institute of Communications and Information Sciences
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• v.41 no.1
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• pp.83-85
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• 2016

The OFDM with LS signal detection performs worse in fast time varying channels as the channel matrix has higher chance of becoming ill-conditioned. Various regularization methods are applied to avoid performance degradation in LS signal detection. In this paper, we proposed a CGLS method with the stopping criteria imposed by the characteristics of the modulation method, which shows performance comparable to that of the optimal LMMSE.

• Communications of the Korean Mathematical Society
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• v.28 no.2
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• pp.407-418
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• 2013

This paper studies a computational iterative method to find accurate approximations for the inverse of real or complex matrices. The analysis of convergence reveals that the method reaches seventh-order convergence. Numerical results including the comparison with different existing methods in the literature will also be considered to manifest its superiority in different types of problems.

• Journal of applied mathematics & informatics
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• v.18 no.1_2
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• pp.621-637
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• 2005

A hybrid method solving regularized structured linear total least norm (RSTLN) problems, which have highly ill-conditioned coefficient matrix with special structures, is suggested and analyzed. This scheme combining RSTLN algorithm and separation by parts guarantees the convergence of parameters and has an advantages in reducing the residual norm and relative error of solutions. Computational tests for problems arisen in signal processing and image formation process confirm that the presenting method is effective for more accurate solutions to (R)STLN problem than the (R)STLN algorithm.

• Journal of the Korean Mathematical Society
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• v.54 no.2
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• pp.613-626
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• 2017

For the overdetermined linear system, when both the data matrix and the observed data are contaminated by noise, Total Least Squares method is an appropriate approach. Since an ill-conditioned data matrix with noise causes a large perturbation in the solution, some kind of regularization technique is required to filter out such noise. In this paper, we consider a Dual regularized Total Least Squares problem. Unlike the Tikhonov regularization which constrains the size of the solution, a Dual regularized Total Least Squares problem considers two constraints; one constrains the size of the error in the data matrix, the other constrains the size of the error in the observed data. Our method derives two nonlinear equations to construct the iterative method. However, since the Jacobian matrix of two nonlinear equations is not guaranteed to be nonsingular, we adopt a trust-region based iteration method to obtain the solution.

• Journal of applied mathematics & informatics
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• v.32 no.1_2
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• pp.171-184
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• 2014

A higher order iterative method to compute the Moore-Penrose inverses of arbitrary matrices using only the Penrose equation (ii) is developed by extending the iterative method described in [1]. Convergence properties as well as the error estimates of the method are studied. The efficacy of the method is demonstrated by working out four numerical examples, two involving a full rank matrix and an ill-conditioned Hilbert matrix, whereas, the other two involving randomly generated full rank and rank deficient matrices. The performance measures are the number of iterations and CPU time in seconds used by the method. It is observed that the number of iterations always decreases as expected and the CPU time first decreases gradually and then increases with the increase of the order of the method for all examples considered.

• Journal of Korea Water Resources Association
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• v.31 no.4
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• pp.439-448
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• 1998

There are many methods to calculate steady-state flowrate in a large water distribution system. Linear method which analyzes continuity equations and energy equations simultaneously is most widely used. Though it is theoretically simple, when it is applied to a practical water distribution system, it produces a very sparse coefficient matrix and most of its diagonal elements are to be zero. This sparsity characteristic of coefficient matrix makes it difficult to analyze pipe flow using the linear method. In this study, a graph theory is introduced to water distribution system analysis in order to prevent from producing ill-conditioned coefficient matrix and the technique is developed to produce positive-definite matrix. To test applicability of developed method, this method is applied to 22 pipes and 142 pipes system located nearby Taegu city. The results obtained from these applications show that the method can calculate flowrate effectively without failure in converage. Thus it is expected that the method can analyze steady state flowrate and pressure in pipe network systems efficiently. Keywords : pipe flow analysis, graph theory, linear method.

• Proceedings of the KOSOMBE Conference
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• v.1991 no.05
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• pp.5-7
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• 1991

We have developed an efficient and robust image reconstruction algorithm for static impedance imaging. This improved Newton-Raphson method produced more accurate images by reducing the undesirable effects of the ill-conditioned Hessian matrix. We found that our electrical impedance tomography (EIT) system could produce two-dimensional static images from a physical phantom with 7% spatial resolution at the center and 5% at the periphery. Static EIT image reconstruction requires a large amount of computation. In order to overcome the limitations on reducing the computation time by algorithmic approaches, we implemented the improved Newton-Raphson algorithm on a parallel computer system and showed that the parallel computation could reduce the computation time from hours to minutes.

• Journal of Mechanical Science and Technology
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• v.17 no.5
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• pp.637-646
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• 2003

In the previous study, the inverse perturbation method was used to identify structural damages. Because all unmeasured DOFs were considered as unknown variables, considerable computational effort was required to obtain reliable results. Thus, in the present study, a system condensation method is used to transform the unmeasured DOFs into the measured DOFs, which eliminates the remaining unmeasured DOFs to improve computational efficiency. However, there may still arise a numerically ill-conditioned problem, if the system condensation is not adequate for numerical Programming or if the system condensation is not recalibrated with respect to the structural changes. This numerical problem is resolved in the present study by adopting more accurate accelerated improved reduced system (AIRS) as well as by updating the transformation matrix at every step. The criterion on the required accuracy of the condensation method is also proposed. Finally, numerical verification results of the present accelerated inverse perturbation method (AIPM) are presented.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.2
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• pp.367-377
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• 2012

The goal of the image restoration is to find a good approximation of the original image for the degraded image, the blurring matrix, and the statistics of the noise vector given. Fast truncated Lagrange (FTL) method has been proposed by G. Landi as a image restoration method for large-scale ill-conditioned BTTB linear systems([3]). We implemented FTL method for the image restoration problem with reflective boundary condition which gives better reconstructions of the unknown, the true image.

• Journal of the Chungcheong Mathematical Society
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• v.31 no.1
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• pp.137-149
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• 2018

In this paper, under the assumption of the symmetry point spread function, antireflective boundary conditions(AR-BCs) are considered in connection with the fast truncated Lagrange(FTL) method. The FTL method is proposed as an image restoration method for large-scale ill-conditioned BTTB(block Toeplitz with Toeplitz block) and BTHHTB(block Toeplitz-plus-Hankel matrix with Toeplitz-plus-Hankel blocks) linear systems([13, 17]). The implementation and efficiency of the FTL method in the AR-BCs are further illustrated. Especially, by employing the AR-BCs, both the continuity of the image and the continuity of its normal derivative are preserved at the boundary. A reconstructed image with less artifacts at the boundary is obtained as a result.