• Title/Summary/Keyword: matrix multiplication

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MULTIPLICATION OPERATORS ON BERGMAN SPACES OVER POLYDISKS ASSOCIATED WITH INTEGER MATRIX

  • Dan, Hui;Huang, Hansong
    • Bulletin of the Korean Mathematical Society
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    • v.55 no.1
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    • pp.41-50
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    • 2018
  • This paper mainly considers a tuple of multiplication operators on Bergman spaces over polydisks which essentially arise from a matrix, their joint reducing subspaces and associated von Neumann algebras. It is shown that there is an interesting link of the non-triviality for such von Neumann algebras with the determinant of the matrix. A complete characterization of their abelian property is given under a more general setting.

A method for intra-prediction in the Integer DCT domain of H.264 (H.264의 integer DCT 영역에서의 Intra-prediction 기법)

  • Ahn, Hyeong-Jin;Oh, Hyung-Suk;Kim, Won-Ha
    • Proceedings of the KIEE Conference
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    • 2008.04a
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    • pp.91-92
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    • 2008
  • 본 논문에서는 기존의 H.264/AVC의 spatial 영역에서 Intra prediction 기법과 달리 H.264/AVC에서 사용하는 Integer DCT 영역에서 Intra prediction 기법을 제안한다. 이를 위하여 Integer DCT 영역에서 Intra prediction을 수행하는 모든 과정을 matrix multiplication으로 표현하여 Intra prediction을 수행하는 matrix를 유도한다. Intra prediction을 수행하는 matrix를 각 모드에 알맞게 설계하고, 이 matrix를 Integer DCT 영역에서 사용할 수 있도록 orthogonal한 Integer matrix를 설계한다. 실험을 통하여 제안한 Integer DCT 영역에서 Intra prediction 기법이 기존의 H.264/AVC의 spatial 영역에서 intra prediction 기법과 성능이 동일하면서 어떻게 matrix multiplication에 연산들을 포함시켜서 단순화 할 수 있는지를 보여주겠다. 또한 H.264/AVC에서 제공하는 intra prediction 각 모드에 대해 계산상 복잡도를 분석하였다.

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A Polynomial-Time Algorithm for Breaking the McEliece's Public-Key Cryptosystem (McEliece 공개키 암호체계의 암호해독을 위한 Polynomial-Time 알고리즘)

  • Park, Chang-Seop-
    • Proceedings of the Korea Institutes of Information Security and Cryptology Conference
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    • 1991.11a
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    • pp.40-48
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    • 1991
  • McEliece 공개키 암호체계에 대한 새로운 암호해독적 공격이 제시되어진다. 기존의 암호해독 algorithm이 exponential-time의 complexity를 가지는 반면, 본고에서 제시되어지는 algorithm은 polynomial-time의 complexity를 가진다. 모든 linear codes에는 systematic generator matrix가 존재한다는 사실이 본 연구의 동기가 된다. Public generator matrix로부터, 암호해독에 사용되어질 수 있는 새로운 trapdoor generator matrix가 Gauss-Jordan Elimination의 역할을 하는 일련의 transformation matrix multiplication을 통해 도출되어진다. 제시되어지는 algorithm의 계산상의 complexity는 주로 systematic trapdoor generator matrix를 도출하기 위해 사용되는 binary matrix multiplication에 기인한다. Systematic generator matrix로부터 쉽게 도출되어지는 parity-check matrix를 통해서 인위적 오류의 수정을 위한 Decoding이 이루어진다.

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GPU-Based ECC Decode Unit for Efficient Massive Data Reception Acceleration

  • Kwon, Jisu;Seok, Moon Gi;Park, Daejin
    • Journal of Information Processing Systems
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    • v.16 no.6
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    • pp.1359-1371
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    • 2020
  • In transmitting and receiving such a large amount of data, reliable data communication is crucial for normal operation of a device and to prevent abnormal operations caused by errors. Therefore, in this paper, it is assumed that an error correction code (ECC) that can detect and correct errors by itself is used in an environment where massive data is sequentially received. Because an embedded system has limited resources, such as a low-performance processor or a small memory, it requires efficient operation of applications. In this paper, we propose using an accelerated ECC-decoding technique with a graphics processing unit (GPU) built into the embedded system when receiving a large amount of data. In the matrix-vector multiplication that forms the Hamming code used as a function of the ECC operation, the matrix is expressed in compressed sparse row (CSR) format, and a sparse matrix-vector product is used. The multiplication operation is performed in the kernel of the GPU, and we also accelerate the Hamming code computation so that the ECC operation can be performed in parallel. The proposed technique is implemented with CUDA on a GPU-embedded target board, NVIDIA Jetson TX2, and compared with execution time of the CPU.

DISTRIBUTIVE PROPERTIES OF ADDITION OVER MULTIPLICATION OF IDEMPOTENT MATRICES

  • Wanicharpichat, Wiwat
    • Journal of applied mathematics & informatics
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    • v.29 no.5_6
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    • pp.1603-1608
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    • 2011
  • Let R be a ring with identity. If a, b, $c{\in}R$ such that a+b+c = 1, then the distributive laws from addition over multiplication hold in R, that is a+(bc) = (a+b)(a+c) when ab = ba, and (ab)+c = (a+c)(b+c) when ac = ca. An application to obtains, if A,B are idempotent matrices and AB = BA = 0 then there exists an idempotent matrix C such that A + BC = (A + B)(A + C), and also A + BC = (I - C)(I - B). Some other cases and applications are also presented.

An Implementation of Digital Neural Network Using Systolic Array Processor (영어 수계를 이용한 디지털 신경망회로의 실현)

  • 윤현식;조원경
    • Journal of the Korean Institute of Telematics and Electronics B
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    • v.30B no.2
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    • pp.44-50
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    • 1993
  • In this paper, we will present an array processor for implementation of digital neural networks. Back-propagation model can be formulated as a consecutive matrix-vector multiplication problem with some prespecified thresholding operation. This operation procedure is suited for the design of an array processor, because it can be recursively and repeatedly executed. Systolic array circuit architecture with Residue Number System is suggested to realize the efficient arithmetic circuit for matrix-vector multiplication and compute sigmoid function. The proposed design method would expect to adopt for the application field of neural networks, because it can be realized to currently developed VLSI technology.

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Shoot multiplication kinetics and hyperhydric status of regenerated shoots of gladiolus in agar-solidified and matrix-supported liquid cultures

  • Gupta, S. Dutta;Prasad, V.S.S.
    • Plant Biotechnology Reports
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    • v.4 no.1
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    • pp.85-94
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    • 2010
  • In vitro shoot regeneration of gladiolus in three different culture systems, viz., semi-solid agar (AS), membrane raft (MR), and duroplast foam liquid (DF) cultures was evaluated following the kinetics of shoot multiplication and hyperhydricity at optimized growth regulator combinations. Compared to the AS system, matrixsupported liquid cultures enhanced shoot multiplication. The peak of shoot multiplication rate was attained at 18 days of incubation in the MR and DF systems, whereas the maximum rate in the AS system was attained at 21 days. An early decline in acceleration trend was observed in liquid cultures than the AS culture. The hyperhydric status of the regenerated shoots in the different culture systems was assessed in terms of stomatal attributes and antioxidative status. Stomatal behavior appeared to be normal in the AS and MR systems. However, structural anomaly of stomata such as large, round shaped guard cells with damage in bordering regions of stomatal pores was pronounced in the DF system along with a relatively higher $K^+$ ion concentration than in the AS and MR systems. Antioxidative status of regenerated shoots was comparable in the AS and MR systems, while a higher incidence of oxidative damages of lipid membrane as evidenced from malondialdehyde and ascorbate content was observed in the DF system. Higher oxidative stress in the DF system was also apparent by elevated activities of superoxide dismutase, ascorbate peroxidase, and catalase. Among the three culture systems, liquid culture with MR resulted in maximum shoot multiplication with little or no symptoms of hyperhydricity. Shoots in the DF system were more prone to hyperhydricity than those in the AS and MR systems. The use of matrix support such as membrane raft as an interface between liquid medium and propagating tissue could be an effective means for rapid and efficient mass propagation with little or no symptoms of hyperhydricity.

Matrix Addition & Scalar Multiplication on the GPU (GPU 기반 행렬 덧셈 및 스칼라 곱셈 알고리즘)

  • Park, Sangkun
    • Journal of Institute of Convergence Technology
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    • v.8 no.1
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    • pp.15-20
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    • 2018
  • Recently a GPU has acquired programmability to perform general purpose computation fast by running thousands of threads concurrently. This paper presents a parallel GPU computation algorithm for dense matrix-matrix addition and scalar multiplication using OpenGL compute shader. It can play a very important role as a fundamental building block for many high-performance computing applications. Experimental results on NVIDIA Quad 4000 show that the proposed algorithm runs 21 times faster than CPU algorithm and achieves performance of 16 GFLOPS in single precision for dense matrices with size 4,096. Such performance proves that our algorithm is practical for real applications.

Efficient Computation of Eta Pairing over Binary Field with Vandermonde Matrix

  • Shirase, Masaaki;Takagi, Tsuyoshi;Choi, Doo-Ho;Han, Dong-Guk;Kim, Ho-Won
    • ETRI Journal
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    • v.31 no.2
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    • pp.129-139
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    • 2009
  • This paper provides an efficient algorithm for computing the ${\eta}_T$ pairing on supersingular elliptic curves over fields of characteristic two. In the proposed algorithm, we deploy a modified multiplication in $F_{2^{4n}}$ using the Vandermonde matrix. For F, G ${\in}$ $F_{2^{4n}}$ the proposed multiplication method computes ${\beta}{\cdot}F{\cdot}G$ instead of $F{\cdot}G$ with some ${\beta}$ ${\in}$ $F^*_{2n}$ because ${\beta}$ is eliminated by the final exponentiation of the ${\eta}_T$ pairing computation. The proposed multiplication method asymptotically requires only 7 multiplications in $F_{2^n}$ as n ${\rightarrow}$ ${\infty}$, while the cost of the previously fastest Karatsuba method is 9 multiplications in $F_{2^n}$. Consequently, the cost of the ${\eta}_T$ pairing computation is reduced by 14.3%.

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Efficient Matrix Multiplication Algorithms and its Application to Development of a High Performance Embedded System (효율적인 행렬 곱 알고리즘 및 이를 활용한 고성능 임베디드 시스템 개발)

  • Kim, Wonsop;Jeon, Wonbo;Gong, Minsik
    • Journal of the Korean Society for Aeronautical & Space Sciences
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    • v.47 no.1
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    • pp.75-80
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    • 2019
  • In the recent aerospace and defence industries, it is required to develop small and low cost embedded systems. Based on a high speed digital signal processor (DSP), this paper first presents the development of an embedded system. To reduce the computation time of the high precision algorithm such as flight control, we also propose two algorithms for matrix multiplication. Validation results show that, compared to the performance using the $2{\times}2$ unit method, the performance of the proposed method 1 is improved, when the size of matrices is small. The proposed method 2 generally outperforms the $2{\times}2$ unit method.