• Honam Mathematical Journal
• /
• v.30 no.2
• /
• pp.399-409
• /
• 2008

We consider the most generalized quadratic matrix equation, Q(X) = $A_7XA_6XA_5+A_4XA_3+A_2XA_1+A_0=0$, where X is m ${\times}$ n, $A_7$, $A_4$ and $A_2$ are p ${\times}$ m, $A_6$ is n ${\times}$ m, $A_5$, $A_3$ and $A_l$ are n ${\times}$ q and $A_0$ is p ${\times}$ q matrices with complex elements. The convergence of Newton's method for solving some different types of quadratic matrix equations are considered and we show that the elementwise minimal positive solvents can be found by Newton's method with the zero starting matrices. We finally give numerical results.

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

• Journal of Radiation Protection and Research
• /
• v.11 no.1
• /
• pp.3-14
• /
• 1986

A stud has been carried out for figuring out real photon spectrum from an observed gamma-ray spectrum by means of response matrix method, which is known one of the relatively convenient method for the estimation of exposure rate of a complex gamma ray field in comparison with graphical analysis and least square fitting of the measured spectrum. A 3'${\times}$3' cylindrical Nal(T1) scintillation detector in association with multichannel pulse height analyzer and six reference gamma ray sources covering the photon energy range of 0.05 to 2.0 MeV were used. In dividing the energy region for the construction of response matrix, two different approaches were attempted. One is dividing the entire energy region of interest into 20 bins, one of which corresponds to a width of 0.1 MeV to form $20{\times}20$ matrix, and another is dividing the 2 MeV region into 14 bins to form $14{\times}14$ matrix consists of $0.1(MeV)^{1/2}$ intervals assuming the resolution of the detector is dependent on square root of the incident photon energy. Inversion of thus constructed matrices was performed by a computor(P-E8/32) using the program attached to the end of this paper. The resultant exposure rates obtained by this method were in good agreement, within 10% with those calculated by ordinary formula widely used for a gamma-ray field of known energy and flux. It is concluded that the photen flux obtained by the response matrix constructed under the assumption of $E^{1/2}$ dependence is more realistic than that obtained by the matrix consist of identical energy bins in dosimetrical point of view.

• Korean Journal of Cognitive Science
• /
• v.22 no.4
• /
• pp.347-364
• /
• 2011

In this paper, we propose a automatic image bases extraction method for visual image reconstruction from brain activity using Non-negative Matrix Factorization (NMF). Image bases are basic elements to construct and present a visual image. Previous method used brain activity that evoked by predefined 361 image bases of four different sizes: $1{\times}1$, $2{\times}1$, $1{\times}2$, $2{\times}2$, and $2{\times}2$. Then the visual stimuli were reconstructed by linear combination of all the results from these image bases. While the previous method used 361 predefined image bases, the proposed method automatically extracts image bases which represent the image data efficiently. From the experiments, we found that the proposed method reconstructs the visual stimuli better than the previous method.

• Journal of the Korean Mathematical Society
• /
• v.50 no.4
• /
• pp.755-770
• /
• 2013

One of the interesting nonlinear matrix equations is the quadratic matrix equation defined by $$Q(X)=AX^2+BX+C=0$$, where X is a $n{\times}n$ unknown real matrix, and A, B and C are $n{\times}n$ given matrices with real elements. Another one is the matrix polynomial $$P(X)=A_0X^m+A_1X^{m-1}+{\cdots}+A_m=0,\;X,\;A_i{\in}\mathbb{R}^{n{\times}n}$$. Newton's method is used to find the symmetric and bisymmetric solvents of the nonlinear matrix equations Q(X) and P(X). The method does not depend on the singularity of the Fr$\acute{e}$chet derivative. Finally, we give some numerical examples.

• Journal of the Korean Society for Aeronautical & Space Sciences
• /
• v.47 no.1
• /
• pp.75-80
• /
• 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.

• Journal of the Korean Ceramic Society
• /
• v.30 no.11
• /
• pp.897-904
• /
• 1993

CdS doped SiO2 glass coating films which are good candidates for the nonlinear optical materials were prepared by the Sol-Gel method. TEOS, C2H5OH, H2O and HCl were used as starting materials to obtain SiO2 matrix solutions. Then Cd(NO3)2.2H2O and CS(NH2)2 were dissolved into the SiO2 matrix solutions. Coating was performed several times in order to increase the thickness of coated film by the dip-coating method. Then heat treatments were carried out to control the size of CdS microcrystals doped in SiO2 glass matrix with respect to temperatures and times. CdS-doped SiO2 transparent coating films were successfully obtained. CdS crystals were changed from cubic to hexagonal type about $600^{\circ}C$.

• Proceedings of the Korea Electromagnetic Engineering Society Conference
• /
• 2003.11a
• /
• pp.79-83
• /
• 2003

Multi-port($2{\times}2$port, 1port) rectangular waveguide discontinuity problem has been analyzed by use of $TE^x_{mn}$ (mono)mode matching method. Matrix size can be reduced significantly in comparison with $TE_{mn}&TM_{mn}$(full-wave)mode matching method. the present results is compared with those by CST MicroWave Studio to validate the presint method.

• Journal of the Korea Society of Computer and Information
• /
• v.17 no.9
• /
• pp.9-16
• /
• 2012

In this paper, we propose the two dimensional variable-length vector storage format which can be used for efficient storage of sparse matrix in the FEM (finite element method). The proposed storage format is the method storing only actual needed non-zero values of each row on upper triangular matrix with the total rows N, by using two dimensional variable-length vector instead of $N{\times}N$ large sparse matrix of entire equation of finite elements. This method only needs storage spaces of the number of minimum 1 to maximum 5 in 2D grid structure and the number of minimum 1 to maximum 14 in 3D grid structure of analysis target. The number doesn't excess two times although involving index number. From the experimental result, we can find out that the proposed storage format can reduce the memory space more effectively, as the total number of nodes increases, than the existing skyline storage format storing maximum column height.

• IEMEK Journal of Embedded Systems and Applications
• /
• v.17 no.6
• /
• pp.367-374
• /
• 2022

The acceleration of neural networks has become an important topic in the field of computer vision. An accelerator is absolutely necessary for accelerating the lightweight model. Most accelerator-supported operators focused on direct convolution operations. If the accelerator does not provide GEMM operation, it is mostly replaced by CPU operation. In this paper, we proposed an optimization technique for 2-stage tiling-based GEMM routines on VTA. We improved performance of the matrix multiplication routine by maximizing the reusability of the input matrix and optimizing the operation pipelining. In addition, we applied the proposed technique to the DarkNet framework to check the performance improvement of the matrix multiplication routine. The proposed GEMM method showed a performance improvement of more than 2.4 times compared to the non-optimized GEMM method. The inference performance of our DarkNet framework has also improved by at least 2.3 times.