• KSII Transactions on Internet and Information Systems (TIIS)
• /
• 제13권11호
• /
• pp.5616-5630
• /
• 2019

Fully homomorphic encryption allows a third-party to perform arbitrary computation over encrypted data and is especially suitable for secure outsourced computation. This paper investigates secure outsourced computation of multiple matrix multiplication based on fully homomorphic encryption. Our work significantly improves the latest Mishra et al.'s work. We improve Mishra et al.'s matrix encoding method by introducing a column-order matrix encoding method which requires smaller parameter. This enables us to develop a binary multiplication method for multiple matrix multiplication, which multiplies pairwise two adjacent matrices in the tree structure instead of Mishra et al.'s sequential matrix multiplication from left to right. The binary multiplication method results in a logarithmic-depth circuit, thus is much more efficient than the sequential matrix multiplication method with linear-depth circuit. Experimental results show that for the product of ten 32×32 (64×64) square matrices our method takes only several thousand seconds while Mishra et al.'s method will take about tens of thousands of years which is astonishingly impractical. In addition, we further generalize our result from square matrix to non-square matrix. Experimental results show that the binary multiplication method and the classical dynamic programming method have a similar performance for ten non-square matrices multiplication.

• Journal of the Korean Statistical Society
• /
• 제36권4호
• /
• pp.457-469
• /
• 2007

Many procedures are available to identify a single outlier or an isolated influential point in linear regression and logistic regression. But the detection of influential points or multiple outliers is more difficult, owing to masking and swamping problems. The multiple outlier detection methods for logistic regression have not been studied from the points of direct procedure yet. In this paper we consider the direct methods for logistic regression by extending the $Pe\tilde{n}a$ and Yohai (1995) influence matrix algorithm. We define the influence matrix in logistic regression by using Cook's distance in logistic regression, and test multiple outliers by using the mean shift model. To show accuracy of the proposed multiple outlier detection algorithm, we simulate artificial data including multiple outliers with masking and swamping.

• 한국해양공학회지
• /
• 제19권5호
• /
• pp.1-15
• /
• 2005

The motion behaviors including hydrodynamic interaction and mechanical coupling effects on multiple-body floating platforms are simulated by using a time domain hull/mooring/riser coupled dynamics analysis program. The objective of this study is to evaluate off-diagonal hydrodynamic interaction effects and mechanical coupling effects on tandem moored FPSO and shuttle taker motions. In the multiple-body floating platforms interaction, hydrodynamic coupling effects with waves and mechanical coupling effects through the connectors should be considered. Thus, in this study, the multiple-body platform motions are calculated by Combined Matrix Method (CMM) as well as Separated Matrix Method (SMM). The advantage of the combined matrix method is that it can include all the 6Nx6N full hydrodynamic and mechanical interaction effects among N bodies. Whereas, due to the larger matrix size, the calculation time of Combined Matrix Method (CMM) is longer than the Separated Matrix Method (SMM). On the other hand, Separated Matrix Method (SMM) cannot include the off-diagonal 6x6 hydrodynamic interaction coefficients although it can fully include mechanical interactions among N bodies. To evaluate hydrodynamic interaction and mechanical coupling effects, tandem moored FPSO and shuttle tanker is simulated by Combined Matrix Method (CMM) and Separated Matrix Method (SMM). The calculation results give a good agreement between Combined Matrix Method (CMM) and Separated Matrix Method (SMM). The results show that the Separated Matrix Method (SMM) is more efficient for tandem moored FPSO and shuttle tanker. In the numerical calculation, the hydrodynamic coefficients are calculated from a 3D diffraction/radiation panel program WAMIT, and wind and current forces are generated by using the respective coefficients given in the OCIMF data sheet.

• 대한전자공학회:학술대회논문집
• /
• 대한전자공학회 2002년도 ITC-CSCC -1
• /
• pp.619-622
• /
• 2002

In this paper, we propose a new blocking method, multiple blocking, and examine the efficiency of the method in basic matrix operations. In the best case for the matrix multiplication C=AB＋C, the multiple blocking improves the performance by more than 10%, compared to the conventional single blocking method.

• Kyungpook Mathematical Journal
• /
• 제56권1호
• /
• pp.57-68
• /
• 2016

In this work, we shall give the degree of approximation for functions belonging to $H{\ddot{o}}lder$ class by matrix summability method of multiple Fourier series in the $H{\ddot{o}}lder$ metric.

• Journal of Communications and Networks
• /
• 제17권6호
• /
• pp.634-646
• /
• 2015

Assuming perfect channel state information (CSI) at the transmitter and receiver, the optimization problem of maximizing the minimum Euclidean distance between two received signals by a linear precoder is considered for multiple-input multiple-output (MIMO) systems with arbitrary dimensions and arbitraryary quadrature amplitude modulation (QAM) input. A general precoding framework is first presented based on the Gram matrix, which is shown for 2-dimensional (2-D) and 3-dimensional (3-D) MIMO systems when employing the ellipse expanding method (EEM). An extended precoder for high-dimensional MIMO system is proposed following the precoding framework, where the Gram matrix for high-dimensional precoding matrix can be generated through those chosen from 2-D and 3-D results in association with a permutation matrix. A complexity-reduced maximum likelihood detector is also obtained according to the special structure of the proposed precoder. The analytical and numerical results indicate that the proposed precoder outperforms the other precoding schemes in terms of both minimum distance and bit error rate (BER).

• Smart Structures and Systems
• /
• 제19권2호
• /
• pp.203-211
• /
• 2017

This paper provides a numerical solution for multiple confocal elliptic dissimilar cylinders. In the problem, the inner elliptic notch is under the traction free condition. The medium is composed of many confocal elliptic dissimilar cylinders. The transfer matrix method is used to study the continuity condition for the stress and displacement along the interfaces. Two cases, or the infinite matrix case and the finite matrix case, are studied in this paper. In the former case, the remote tension is applied in y- direction. In the latter case, the normal loading is applied along the exterior elliptic contour. For two cases, several numerical results are provided.

• 한국소음진동공학회논문집
• /
• 제12권9호
• /
• pp.709-716
• /
• 2002

A practical method of predicting the sound absorption coefficient for multiple perforated-plate sound absorbing system was developed using transfer matrix method. The proposed method was validated by comparing the calculated absorption coefficients of a single layer perforated plate with the values measured by the two-microphone impedance tube method for various porosity and spacing of the perforated plate. The developed transfer matrix method was further applied to estimate the multiple layer perforated plates and it is shown that the estimated absorption coefficients agree well with the measured values.

• 한국소음진동공학회:학술대회논문집
• /
• 한국소음진동공학회 2001년도 추계학술대회논문집 II
• /
• pp.653-658
• /
• 2001

In this study, a new practical method of predicting the sound absorption coefficient for multiple perforated-plate sound absorbing system was developed using transfer matrix method. In order to validate the proposed method, the absorption coefficients calculated by transfer matrix method for single perforated plate were first compared with the absorption coefficients measured by SWR method according to different porosity, hole diameter, and thickness of the perforated plate. Based on the comparison results, transfer matrix method was further applied to double and triple perforated plates to evaluate the absorption coefficients. The experimental results showed that the absorption coefficients from transfer matrix method generally agreed well with the corresponding absorption coefficients from SWR method. However, due to the limitations of the impedance model used in this study, the measured values were differed with the calculated values for small porosity, hole diameter, and thickness in size of the perforated plate indicating the need of impedance model development for multiple perforated-plate sound absorbing system covering wide ranges of porosity, hole diameter, and thickness of the perforated plate.

• 한국통신학회논문지
• /
• 제33권12A호
• /
• pp.1185-1190
• /
• 2008

이 논문에서는 IST (information society technologies)-WINNER (wireless world initiative new radio) 프로젝트에서 MU-MIMO (multiuser multiple-input multiple-output) 프리코딩 방식으로 채택된 SMMSE (successive minimum mean square error) 프리코딩 방법의 프리코딩 행렬 생성을 단순화하기 위한 $S^{2}MMSE$ (simplified SMMSE) 알고리즘을 제안한다. 기존의 알고리즘이 모든 사용자들의 모든 수신 안테나들을 대상으로 개별 MMSE nulling을 필요로 하는 프리코멍 벡터들을 생성하는 것과 대조적으로, 제안되는 알고리즘은 먼저 사용자 별 MMSE nulling 과정을 수행하고, 해당 사용자 내에서는 이 결과를 공통으로 이용하여 개별 수신 안테나에서 추가적인 MMSE nulling 과정 없이 단순한 행렬-벡터 곱으로 프리코딩 벡터를 계산한다. 따라서, 이 알고리즘을 사용하면 SMMSE 프리코딩을 위한 프리코멍 행렬 생성을 크게 단순화시킬 수 있다.