• Proceedings of the KIEE Conference
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• 2003.07a
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• pp.110-112
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• 2003

This paper presents an alleviant technique for solving ill-conditioned linear systems using spectral adaptive mapping, which is based on spectral mapping theorem. The conventional approaches to solve the ill-conditioned linear systems are divided into reformulation and alleviant technique. So far, the alleviant technique is evaluated the most effective one. In this paper, an adaptive mapping of spectrum is adopted to alleviate the condition number of ill-conditioned linear systems. A shift constant, which is a dominant factor of the spectral adaptive mapping that are proposed, is assessed by the system spectrum. The proposed spectral adaptive mapping technique is tested to demonstrated the validation on several size Hilbert matrices and small scale power systems, which are provide the promising results.

• Journal of the Korean Mathematical Society
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• v.48 no.5
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• pp.939-952
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• 2011

This paper is concerned with the solution of ill-conditioned Systems of Linear Equations (SLE's) via the solution of equivalent SLE's which are well-conditioned. A matrix is rst constructed from that of the given ill-conditioned system. Then, an adequate right-hand side is computed to make up the instance of an equivalent system. Formulae and algorithms for computing an instance of this equivalent SLE and solving it will be given and illustrated.

• Journal of Institute of Control, Robotics and Systems
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• v.7 no.12
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• pp.1001-1008
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• 2001

This paper presents a new camera calibration algorithm for ill-conditioned cases in which the camera plane is nearly parallel to a set of non-coplanar calibration boards. for the ill-conditioned case, most of existing calibration approaches such as Tsais radial-alignment-constraint method cannot be applied. Recently, for the ill-conditioned coplanar calibration Lee&Lee[16] proposed an iterative algorithm based on the least square method. The non-coplanar calibration algorithm presented in this paper is an iterative two-stage procedure with extends the previous coplanar calibration algorithm. Through the first stage, camera, position and orientation parameters as well as one radial distortion factor are determined optimally for a given data of the scale factor and the focal length. In the second stage, the scale factor and the focal length are locally optimized. This process is repeated until any improvement cannot be expected any more Computational results are provided to show the performance of the algorithm developed.

• Journal of applied mathematics & informatics
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• v.27 no.3_4
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• pp.621-638
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• 2009

The linear system Ax = b will have (i) no solution, (ii) only one non-trivial (trivial) solution, or (iii) infinity of solutions. Our focus will be on cases (ii) and (iii). The mathematical models of many real-world problems give rise to (a) ill-conditioned linear systems, (b) singular linear systems (A is singular with all its linearly independent rows are sufficiently linearly independent), or (c) ill-conditioned singular linear systems (A is singular with some or all of its strictly linearly independent rows are near-linearly dependent). This article highlights the scope and need of a randomized algorithm for ill-conditioned/singular systems when a reasonably narrow domain of a solution vector is specified. Further, it stresses that with the increasing computing power, the importance of randomized algorithms is also increasing. It also points out that, for many optimization linear/nonlinear problems, randomized algorithms are increasingly dominating the deterministic approaches and, for some problems such as the traveling salesman problem, randomized algorithms are the only alternatives.

• 제어로봇시스템학회:학술대회논문집
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• 1997.10a
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• pp.1762-1765
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• 1997

Some ill-conditioned processes are very sensitive to small element-wise uncertainties arising in classical element-by-element model identifications. For such processes, accurate identification of simgular values and right singular vectors are more important than theose of the elements themselves. Singular values and right singular vectors can be found by iteraive identification methods which implement the input and output transformations iteratively. Methods based on SVD decomposition, QR decomposition and LU decomposition are proposed and compared with the Kuong and Mac Gregor's method. Convergence proofs are given. These SVD and QR mehtods use normal matrices for the transformations which cannot be calculated analytically in general and so they are hoard to apply to dynamic processes, whereas the LU method used simple analyitc transformations and can be directly applied to dynamic processes.

• Journal of the Korean Society for Precision Engineering
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• v.16 no.2 s.95
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• pp.164-175
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• 1999

If the camera plane is nearly parallel to the calibration board on which objects are defined, most of existing calibration approaches such as Tsai's radial-alignment-constraint method cannot be applied. Recently, for such an ill-conditioned case, Zhuang & Wu suggested the linear two-stage calibration algorithm assuming that the exact values of focal length and scale factor are known a priori. In this paper, we developed an iterative two-stage algorithm starts with initial guess fo the two parameters to determine the value of the others using Zhuang & Wu's method. In the second stage, the two parameters are locally optimized. This process is repeated until any improvement cannot be expected any more. The performance comparison between Zhuang & Wu's method and our algorithm shows the superiority of ours. Also included are the computational results for the effects of the distribution and the number of calibration points on the calibration performance.

• International Journal of Naval Architecture and Ocean Engineering
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• v.6 no.1
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• pp.175-185
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• 2014

This study presents the prediction of propagated wave profiles using the wave information at a fixed point. The fixed points can be fixed in either space or time. Wave information based on the linear wave theory can be expressed by Fredholm integral equation of the first kinds. The discretized matrix equation is usually an ill-conditioned system. Tikhonov regularization was applied to the ill-conditioned system to overcome instability of the system. The regularization parameter is calculated by using the L-curve method. The numerical results are compared with the experimental results. The analysis of the numerical computation shows that the Tikhonov regularization method is useful.

• Proceedings of the KIPE Conference
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• 2017.07a
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• pp.100-101
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• 2017

This paper presents the dynamics of the current-mode controlled buck and boost converters, which are both connected to an ill-conditioned source. This paper investigates the origin of potential instability and demonstrates internal/external dynamics of the converters under adverse interactions with the source.

• The Journal of the Acoustical Society of Korea
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• v.23 no.1E
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• pp.3-9
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• 2004

An important inverse problem in the field of acoustics is that of reconstructing the strengths of a number of sources given a model of transmission paths from the sources to a number of sensors at which measurements are made. In dealing with this kind of the acoustical inverse problem, strengths of the discretised source distribution can be simply deduced from the measured pressure field data and the inversion of corresponding matrix of frequency response functions. However, deducing :he solution of such problems is not straightforward due to the practical difficulty caused by their inherent ill-conditioned behaviour. Therefore, in order to overcome this difficulty associated with the ill-conditioning, the problem is replaced by a nearby well-conditioned problem whose solution approximates the required solution. In this paper a microphone array are identified for which the inverse problem is optimally conditioned, which can be robust to contaminating errors. This involves sampling both source and field in a manner which results in the discrete pressures and source strengths constituting a discrete Fourier transform pair.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.26 no.6
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• pp.1114-1119
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• 2002

In this paper, the well-conditioned observer is designed to be insensitive to the ill-conditioning factors in transient and steady-state observer performance. A condition number based on 12-norm of the eigenvector matrix of the observer matrix has been proposed on a principal index in the observer performance. For the well-conditioned observer design, the non-normality measure and the observability condition of the observer matrix are utilized. The two constraints are specified into observer gain boundary region that guarantees a small condition number and a stable observer. The observer gain selected in this region guarantees a well-conditioned and observable property. In this study, this method is applied to the Luenberger observer and Kalman filters for small order systems. In designing Kalman filters, the ratio of the process noise covariance to the measurement noise covariance is a design parameter and its effect on the condition number is investigated.