• Journal of applied mathematics & informatics
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• v.8 no.2
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• pp.651-658
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• 2001

The projection matrix plays an important role in the linear model theory. In this paper we derive an algebraic relationship between the projection matrices of submatrices of the design matrix. Using this relationship we can easily obtain the projection matrices of any submatrices of the design matrix. Also we show that every projection matrix can be obtained as a linear combination of Kronecker products of identity matrices and matrices with all elements equal to 1.

• International Journal of Automotive Technology
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• v.2 no.3
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• pp.117-122
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• 2001

For a dynamic analysis of a constrained multibody system, it is necessary to have a routine for satisfying kinematic constraints. LU decomposition scheme, which is used to divide coordinates into dependent and independent coordinates, is efficient but has great difficulty near the singular configuration. Other method such as the projection matrix, which is more stable near a singular configuration, takes longer simulation time due to the large amount of calculation for decomposition. In this paper, the row space and the null space of the Jacobian matrix are proposed by using the pseudo-inverse method and the projection matrix. The equations of the motion of a system are replaced with independent acceleration components using the null space of the Jacobian matrix. Also a new hybrid method is proposed, combining the LU decomposition and the projection matrix. The proposed hybrid method has following advantages. (1) The simulation efficiency is preserved by the LU method during the simulation. (2) The accuracy of the solution is also achieved by the projection method near the singular configuration.

• Bulletin of the Korean Mathematical Society
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• v.59 no.5
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• pp.1215-1235
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• 2022

In this paper we study Szegö kernel projections for Hardy spaces in quaternionic Clifford analysis. At first we introduce the matrix Szegö projection operator for the Hardy space of quaternionic Hermitean monogenic functions by the characterization of the matrix Hilbert transform in the quaternionic Clifford analysis. Then we establish the Kerzman-Stein formula which closely connects the matrix Szegö projection operator with the Hardy projection operator onto the Hardy space, and we get the matrix Szegö projection operator in terms of the Hardy projection operator and its adjoint. At last, we construct the explicit matrix Szegö kernel function for the Hardy space on the sphere as an example, and get the solution to a Diriclet boundary value problem for matrix functions.

• Journal of the Korean Statistical Society
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• v.22 no.2
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• pp.249-258
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• 1993

It is well known that design matrix X for any factorial design can be represented by a product $X = TX_o$ where T is replication matrix and $X_o$ is the corresponding balanced design matrix. Since $X_o$ consists of regular arrangement of 0's and 1's, we can easily find the spectral decomposition of $X_o',X_o$. Also using this we propose an efficient algorithm for computing the orthogonal projection matrix for a balanced factorial design.

• ETRI Journal
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• v.37 no.6
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• pp.1251-1258
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• 2015

We investigate an image recovery method for sparse-view computed tomography (CT) using an iterative shrinkage algorithm based on a second-order approach. The two-step iterative shrinkage-thresholding (TwIST) algorithm including a total variation regularization technique is elucidated to be more robust than other first-order methods; it enables a perfect restoration of an original image even if given only a few projection views of a parallel-beam geometry. We find that the incoherency of a projection system matrix in CT geometry sufficiently satisfies the exact reconstruction principle even when the matrix itself has a large condition number. Image reconstruction from fan-beam CT can be well carried out, but the retrieval performance is very low when compared to a parallel-beam geometry. This is considered to be due to the matrix complexity of the projection geometry. We also evaluate the image retrieval performance of the TwIST algorithm -sing measured projection data.

• Economic and Environmental Geology
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• v.17 no.4
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• pp.283-288
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• 1984

Projection method has been used in the phase equilibria study. The projection is made through the saturated phase on the smaller chemical system from larger system. This decreases the number of phases which are included in the larger chemical system. In multiple projection containing plagioclase as a projection phase, there is a difference in matrix calculation when plagioclase is treated as a single composite component and separately as an albite and anorthite. The matrix calculation is considered to be more usable and easier in multiple projection. The value of the A component in the AFM system, which is the smaller system projected from the larger one, is effected and varies according to the change in the An content in plagioclase that is examined as an example.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.17 no.2
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• pp.471-485
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• 2023

As data sharing increases explosively, such information encoded in QR code is completely public as private messages are not securely protected. This paper proposes a new 'PROMISE' framework for hiding information based on the QR code projection matrix by using image segmentation without modifying the essential QR code characteristics. Projection matrix mapping, matrix scrambling, fusion image segmentation and steganography with SEL(secret embedding logic) are part of the PROMISE framework. The QR code could be mapped to determine the segmentation site of the fusion image as a binary information matrix. To further protect the site information, matrix scrambling could be adopted after the mapping phase. Image segmentation is then performed on the fusion image and the SEL module is applied to embed the secret message into the fusion image. Matrix transformation and SEL parameters should be uploaded to the server as the secret key for authorized users to decode the private message. And it was possible to further obtain the private message hidden by the framework we proposed. Experimental findings show that when compared to some traditional information hiding methods, better anti-detection performance, greater secret key space and lower complexity could be obtained in our work.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.52 no.9
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• pp.550-556
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• 2003

Price-based unit commitment is one of bidding strategies which a Genco may take in a practical manner. For that purpose, it is required for a Genco to decide output levels of its generators at each trade period. In this paper, an economic dispatch of thermal units is proposed considering the quantity of reserve contracts. A gradient projection algorithm is adopted as an optimization tool. A direct form of a projection matrix without any calculation of matrix inverse and multiplications is induced. Besides, it is proved that there is no need to check one of the two optimality conditions in the gradient projection method, which also requires matrix inverse and multiplications.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.22 no.1
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• pp.170-176
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• 1998

In this paper, the column space and null space of the Jacobian matrix were obtained by using the pseudo-inverse method and projection matrix. The equations of motion of the system were replaced by independent acceleration components using the null space matrix. The proposed method has the following advantages. (1) It is simple to derive the null space. (2) The efficiency is improved by getting rid of constrained force terms. (3) Neither null space updating nor coordinate partitioning method is required. The suggested algorithm is applied to a three-dimensional vehicle model to show the efficiency.

• Journal of the Korean Mathematical Society
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• v.52 no.2
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• pp.349-372
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• 2015

This paper concerns with exploiting an oblique projection technique to solve a general class of large and sparse least squares problem over symmetric arrowhead matrices. As a matter of fact, we develop the conjugate gradient least squares (CGLS) algorithm to obtain the minimum norm symmetric arrowhead least squares solution of the general coupled matrix equations. Furthermore, an approach is offered for computing the optimal approximate symmetric arrowhead solution of the mentioned least squares problem corresponding to a given arbitrary matrix group. In addition, the minimization property of the proposed algorithm is established by utilizing the feature of approximate solutions derived by the projection method. Finally, some numerical experiments are examined which reveal the applicability and feasibility of the handled algorithm.