• The Journal of the Korea institute of electronic communication sciences
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• v.12 no.1
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• pp.101-108
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• 2017

As the quantum gate matrix is a $r^{n+1}{\times}r^{n+1}$ dimension when the radix is r, the number of control state vectors is n, and the number of target state vectors is one, the matrix dimension with increasing n is exponentially increasing. If the number of control state vectors is $2^n$, then the number of $2^n-1$ unit matrix operations preserves the output from the input, and only one can be performed the unitary operation to the target state vector. Therefore, this paper proposes a new method of function embedding that can replace $2^n-1$ times of unit matrix operations with deterministic contribution to matrix dimension by arithmetic power switch of the unitary gate. The proposed function embedding method uses a binary literal switch with a multivalued threshold, so that a general purpose hybrid MCU gate can be realized in a $r{\times}r$ unitary matrix.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.18 no.12
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• pp.1928-1934
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• 1993

This paper presents a fast algorithm of integer discrete cosine transform(IDCT) allowing VLSI implementation by integer arithmetic. The proposed fast algorithm has been developed using Chen`s matrix decomposition in DCT, and requires less number of arithmetic operations compared to the IDCT. In the presented algorithm, the number of addition number is the same as the one of Chen`s algorithm if DCT, and the number of multiplication if the same as that in DCT at N=8 but drastically decreasing when N is above 8. In addition, the drawbacks of DCT such as performance degradation at the finite length arithmetic could be overcome by the IDCT.

• Journal of the Korea Society of Computer and Information
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• v.4 no.4
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• pp.94-100
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• 1999

This paper concerns the implementation of a digital neural network which performs the high speed operation of Hopfield model's arithmetic operation. It is also designed to use a look-up table and produce floating point arithmetic of nonlinear function with high speed operation. The arithmetic processing of Hopfleld is able to describe the matrix-vector operation, which is adaptable to design the array processor because of its recursive and iterative operation .The proposed method is expected to be applied to the field of real neural networks because of the realization of the current VLSI techniques.

• Journal of applied mathematics & informatics
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• v.5 no.3
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• pp.717-734
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• 1998

In the present paper is presented a new matrix pencil-based numerical approach achieving the computation of the elemen-tary divisors of a given matrix $A \in C^{n\timesn}$ This computation is at-tained without performing similarity transformations and the whole procedure is based on the construction of the Piecewise Arithmetic Progression Sequence(PAPS) of the associated pencil $\lambda I_n$ -A of matrix A for all the appropriate values of $\lambda$ belonging to the set of eigenvalues of A. This technique produces a stable and accurate numerical algorithm working satisfactorily for matrices with a well defined eigenstructure. The whole technique can be applied for the computation of the first second and Jordan canonical form of a given matrix $A \in C^{n\timesn}$. The results are accurate for matrices possessing a well defined canonical form. In case of defective matrices indications of the most appropriately computed canonical form. In case of defective matrices indication of the most appropriately computed canonical form are given.

• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.457-473
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• 2005

In each step of the quasi-minimal residual (QMR) method which uses a look-ahead variant of the nonsymmetric Lanczos process to generate basis vectors for the Krylov subspaces induced by A, it is necessary to decide whether to construct the Lanczos vectors $v_{n+l}\;and\;w{n+l}$ as regular or inner vectors. For a regular step it is necessary that $D_k\;=\;W^{T}_{k}V_{k}$ is nonsingular. Therefore, in the floating-point arithmetic, the smallest singular value of matrix $D_k$, ${\sigma}_min(D_k)$, is computed and an inner step is performed if $\sigma_{min}(D_k)<{\epsilon}$, where $\epsilon$ is a suitably chosen tolerance. In practice it is absolutely impossible to choose correctly the value of the tolerance $\epsilon$. The subject of this paper is to show how discrete stochastic arithmetic remedies the problem of this tolerance, as well as the problem of the other tolerances which are needed in the other checks of the QMR method with the estimation of the accuracy of some intermediate results. Numerical examples are used to show the good numerical properties.

• Proceedings of the Korea Multimedia Society Conference
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• 2003.11b
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• pp.933-936
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• 2003

본 논문은 비트 매트릭스(bit matrix) 확률 모델과 이를 입력으로 사용하는 개량된 이진 산술부호 알고리즘을 제안한다. 비트들로 이루어진 비트 평면에서 3$\times$3 비트 매트릭스를 정의하였다. 그리고 비트 평면을 조사하여 2연속 혹은 3연속 비트 매트릭스들에 대한 확률모델을 구하였다. 본 연구에서는 3 가지의 확률간격(interval)을 가지는 개량된 이진 산술부호기률 사용하였다. 개량된 이진 산술부호 알고리즘의 장점은 구조가 간결하고 또한 부호화가 진행되는 도중에 결과 비트스트림을 생성하는 특징이 있다. 이진 산술부호기는 2연속 혹은 3연속 비트매트릭스를 입력하여 산술부호화를 수행하도록 한다.

• 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.

• Communications of the Korean Institute of Information Scientists and Engineers
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• v.5 no.2
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• pp.85-89
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• 1987

The large sparse matrix problems arise in many applications areas, such as structural analysis, network analysis. In dealing with such sparse systems proper preprogramming techniques such as permuting rows and columns simultaneously, will be needed in order to reduce the number of arithmetic operations and storage spaces.

• Journal of Korea Multimedia Society
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• v.17 no.8
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• pp.953-960
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• 2014

In Shamir's (t,n)-threshold based secret image sharing schemes, there exists a problem that the secret image can be reconstructed when an arbitrary attacker becomes aware of t secret image pieces, or t participants are malicious collusion. It is because that utilizes linear combination polynomial arithmetic operation. In order to overcome the problem, we propose a secret image sharing scheme using matrix decomposition and adversary structure. In the proposed scheme, there is no reconstruction of the secret image even when an arbitrary attacker become aware of t secret image pieces. Also, we utilize a simple matrix decomposition operation in order to improve the security of the secret image. In experiments, we show that performances of embedding capacity and image distortion ratio of the proposed scheme are superior to previous schemes.

• Korean Management Science Review
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• v.11 no.3
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• pp.1-11
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• 1994

Recent advances in linear programming solution methodology have focused on interior point methods. This powerful new class of methods achieves significant reductions in computer time for large linear programs and solves problems significantly larger than previously possible. These methods can be examined from points of Fiacco and McCormick's barrier method, Lagrangian duality, Newton's method, and others. This study presents a primal-dual log barrier algorithm of interior point methods for linear programming. The primal-dual log barrier method is currently the most efficient and successful variant of interior point methods. This paper also addresses a Cholesky factorization method of symmetric positive definite matrices arising in interior point methods. A special structure of the matrices, called supernode, is exploited to use computational techniques such as direct addressing and loop-unrolling. Two dense matrix handling techniques are also presented to handle dense columns of the original matrix A. The two techniques may minimize storage requirement for factor matrix L and a smaller number of arithmetic operations in the matrix L computation.