• Journal of the Chungcheong Mathematical Society
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• v.29 no.1
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• pp.137-150
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• 2016

We introduce a new approach that allows us to solve, algorithmically, the contractive completion problem. In this article, we provide concrete necessary and sufficient conditions for the existence of contractive completions of Hankel partial contractions of size $4{\times}4$ using a Moore-Penrose inverse of a matrix.

• Transactions of the Korean Society of Machine Tool Engineers
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• v.13 no.2
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• pp.120-126
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• 2004

This study proposed the analysis of mass position detection due to the change of the mass and strifeless of structure by using the original and modified dynamic characteristics. The method is applied to examples of the cantilevers beam and the 3 degrees of freedom system by modifying the mass. The predicted detection of the mass positions and magnitudes are in good agrement with the present study from the structural reanalysis using the modified mass.

• Communications of the Korean Mathematical Society
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• v.13 no.4
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• pp.875-888
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• 1998

The use of the zeros of Chebyshev polynomial of the first kind $T_{4n＋4(x}$ ) and second kind $U_{2n＋1}$ (x) for Gauss-Chebyshev quad-rature and collocation of singular integral equations of Cauchy type yields computationally accurate solutions over other combinations of $T_{n}$ /(x) and $U_{m}$(x) as in [8]. We show that the coefficient matrix of the overdetermined system has the generalized inverse. We estimate the residual error using the norm of the generalized inverse.e.

• Communications of the Korean Mathematical Society
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• v.37 no.3
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• pp.705-718
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• 2022

In this paper, for bounded linear operators A, B, C satisfying [AB, B] = [BC, B] = [AB, BC] = 0 we study the Drazin invertibility of the sum of products formed by the three operators A, B and C. In particular, we give an explicit representation of the anti-commutator {A, B} = AB + BA. Also we give some conditions for which the sum A + C is Drazin invertible.

• Proceedings of the Korean Statistical Society Conference
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• 2005.05a
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• pp.135-140
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• 2005

• Journal of the Society of Naval Architects of Korea
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• v.31 no.3
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• pp.31-37
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• 1994

When a lot of input data are not distributed uniformly n a chord-span direction or when the given shape is complicated, it is very difficult to obtain an inverse matrix which represents the smooth Bi-cubic B-spline surface of the initial shape. To overcome this problem, we suggest image Surface Expansion Method(ISE Method) which is suggested for vertex creation of B-spline curves and surfaces. Its basic concept, convergency and verification are shown. Also B-spline curves and Surfaces represented by ISE Method were compared with those represented by the existing method which is based on the inverse matrix method, the pseudoinverse matrix method and the chord length approximation method for vertex yielding. Ship Hull Forms which have Knuckle, Bulbous Bow, Transom and Stern frame were represented by the ISE Method.

• Bulletin of the Korean Mathematical Society
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• v.41 no.1
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• pp.125-135
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• 2004

One of the intriguing and fundamental algorithmic graph problems is the computation of the strongly connected components of a directed graph G. In this paper we first introduce a simple procedure for determining the location of the nonzero elements occurring in $B^{-1}$ without fully inverting B, where EB\;{\equiv}\;(b_{ij)\;and\;B^T$ are diagonally dominant matrices with $b_{ii}\;>\;0$ for all i and $b_{ij}\;{\leq}\;0$, for $i\;{\neq}\;j$, and then, as an application, show that all of the strongly connected components of a directed graph G can be recognized by the location of the nonzero elements occurring in the matrix $C(G)\;=\;(D\;-\;A(G))^{-1}$. Here A(G) is an adjacency matrix of G and D is an arbitrary scalar matrix such that (D - A(G)) becomes a diagonally dominant matrix.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.48 no.5
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• pp.96-101
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• 2011

It is well known that the Capon algorithm offers better resolution compared to that of the FM (Fourier method) algorithm by minimizing the total output power while maintaining a constant gain in the look direction. Unfortunately, the DoA (Direction of Arrival) estimation performance of the Capon algorithm is drastically degraded when the SNR of received signal is low and thus, it cannot distinguish among signal sources which have similar incidence angles. In this paper, we propose a novel scheme enhancing the resolution of the Capon algorithm by ing all rows except the first row of an inverse covariance matrix.

• Transactions of the Korean Society of Automotive Engineers
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• v.16 no.6
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• pp.33-38
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• 2008

Most structures of vehicle are composed of many substructures connected to one another by various types of mechanical joints. In vehicle engineering, it is important to study these jointed structures under random frequency vibration for the evaluations of fatigue life and stress concentration exactly. It is rarely obtained the accurate load history of specified positions in a jointed structure because of the errors such as modeling, measurement, and etc. In the beginning of design, exact load data are actually necessary for the fatigue strength and life analysis to minimize the cost and time of designing. In this paper, the hybrid method of practical dynamic load determination is developed by the combination of the principal stresses from F. E. Analysis and test of a jointed structure. Least square pseudo inverse matrix is adopted to obtain an inverse matrix of analyzed stresses matrix. The error minimization method utilizes the inaccurate measured error and the shifting error that the whole data is stiffed over real data. The least square criterion is adopted to avoid these errors. Finally, to verify the proposed system, a heavy-duty bus is analyzed. This measurement and prediction technology can be extended to the different jointed structures.

• Journal of the Institute of Convergence Signal Processing
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• v.12 no.3
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• pp.163-168
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• 2011

In this paper, we proposed non-linear gamma curve algorithm for gamma correction. The previous non-linear gamma curve algorithm is generated by the least square polynomial using the Gauss-Jordan inverse matrix. However, the previous algorithm has some weak points. When calculating coefficients using inverse matrix of higher degree, occurred truncation errors. Also, only if input sample points are existed regular interval on 10-bit scale, the least square polynomial is accurately works. To compensate weak-points, we calculated accurate coefficients of polynomial using eigenvalue and orthogonal value of mat11x from singular value decomposition (SVD) and QR decomposition of vandemond matrix. Also, we used input data part segmentation, then we performed polynomial curve fitting and merged curve fitting results. When compared the previous method and proposed method using the mean square error (MSE) and the standard deviation (STD), the proposed segmented polynomial curve fitting is highly accuracy that MSE under the least significant bit (LSB) error range is approximately $10^{-9}$ and STD is about $10^{-5}$.