• Journal of applied mathematics & informatics
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• v.7 no.2
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• pp.439-451
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• 2000

To compute derivatives using matrix vector multiplication method, new algorithms were introduced in [1.2]n By these algorithms, we reduced roundoff error in computing derivative using Chebyshev collocation methods (CCM). In this paper, some applications of these algorithms ar presented.

• Journal of Applied and Pure Mathematics
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• v.6 no.1_2
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• pp.37-45
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• 2024

The aim of this article is to consider the sequences generated by repeatedly performing matrix multiplication operations, define the stable, amicable pair, sociable matrix sequences, and analyze the results obtained through iteration. Lastly, numbers are changed to colors to make them easier to understand.

• Proceedings of the Korea Contents Association Conference
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• 2005.11a
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• pp.389-392
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• 2005

Boolean matrices are applied to a variety of areas and used successfully in many applications. There are many researches on the application and multiplication of boolean matrices. Most researches deal with the multiplication of boolean matrices, but all of them focus on the multiplication of just two boolean matrices and very few researches deal with the multiplication of many pairs of two boolean matrices. The paper discusses it is not suitable to use for the multiplication of many pairs of two boolean matrices the algorithm for the multiplication of two boolean matrices that is considered optimal up to now, and suggests a method that can improve the multiplication of a $n{\times}m$ boolean matrix and all $m{\times}k$ boolean matrices.

• Korean Journal of Mathematics
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• v.29 no.4
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• pp.665-677
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• 2021

The main object of this study is to introduce the spaces $c_0({\hat{F}^q)$ and $c({\hat{F}^q)$ derived by the matrix ${\hat{F}^q$ which is the multiplication of Riesz matrix and Fibonacci matrix. Moreover, we find the 𝛼-, 𝛽-, 𝛾- duals of these spaces and give the characterization of matrix classes (${\Lambda}({\hat{F}^q)$, Ω) and (Ω, ${\Lambda}({\hat{F}^q)$) for 𝚲 ∈ {c₀, c} and Ω ∈ {ℓ₁, c₀, c, ℓ_∞}.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.39 no.11
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• pp.1146-1152
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• 1990

Direct calculation algorithm for the nonzero elements of system matrix is suggested for a single machine connected to the infinite bus. Excitation system and power system stabilizer are included. When the system matrix is partitioned into 15 nonzero blocks, we can identify the location of nonzero elements and formula for each element. No matrix inversion and multiplication are necessary. Sensitivity coefficients with respect to controller parameters are suggested based on the structure of system matrix.

• Honam Mathematical Journal
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• v.33 no.3
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• pp.301-310
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• 2011

In this paper, we construct the sets of fuzzy matrix pairs. These sets are naturally occurred at the extreme cases for the zero-term rank inequalities derived from the multiplication of fuzzy matrix pairs. We characterize the linear operators that preserve these extreme sets of fuzzy matrix pairs.

• Journal of Information Technology Services
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• v.6 no.1
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• pp.151-158
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• 2007

D-class computation requires multiplication of three Boolean matrices for each of all possible triples of $n{\times}n$ Boolean matrices and search for equivalent $n{\times}n$ Boolean matrices according to a specific equivalence relation. It is easy to see that even multiplying all $n{\times}n$ Boolean matrices with themselves shows exponential time complexity and D-Class computation was left an unsolved problem due to its computational complexity. The vector-based multiplication theory shows that the multiplication of three Boolean matrices for each of all possible triples of $n{\times}n$ Boolean matrices can be done much more efficiently. However, D-Class computation requires computation of equivalent classes in addition to the efficient multiplication. The paper discusses a theory and an algorithm for efficient D-class computation, and shows execution results of the algorithm.

• Proceedings of the KIEE Conference
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• 1989.07a
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• pp.216-220
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• 1989

Direct calculation algorithm for the elements of A matrix is suggested for a single machine connected to the infinite bus. Excitation system and power system stabilizer are included. When A matrix is partitioned into seven submatrices, we can identify the location of non-zero elements and formula for each element. No matrix inversion and multiplication are necessary.

• Journal of the Institute of Electronics Engineers of Korea SD
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• v.46 no.10
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• pp.61-69
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• 2009

This paper presents the design results of a low complexity and high throughput LDPC encoder structure. In order to solve the high complexity problem of the LDPC encoder, a simplified matrix-vector multiplier is proposed instead of the conventional complex matrix-vector multiplier. The proposed encoder also adopts a partially parallel structure and performs column-wise operations in matrix-vector multiplication to achieve high throughput. Implementation results show that the proposed architecture reduces the number of logic gates and memory elements by 37.4% and 56.7%, compared with existing five-stage pipelined architecture. The proposed encoder also supports 800Mbps throughput at 40MHz clock frequency which is improved about three times more than the existing architecture.

• Journal of the Korea Institute of Military Science and Technology
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• v.21 no.4
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• pp.437-446
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• 2018

This paper describes the real-time logic implementation of orthogonal matching pursuit(OMP) algorithm for compressive sensing digital receiver. OMP contains various complex-valued linear algebra operations, such as matrix multiplication and matrix inversion, in an iterative manner. Xilinx Vivado high-level synthesis(HLS) is introduced to design the digital logic more efficiently. The real-time signal processing is realized by applying dataflow architecture allowing functions and loops to execute concurrently. Compared with the prior works, the proposed design requires 2.5 times more DSP resources, but 10 times less signal reconstruction time of $1.024{\mu}s$ with a vector of length 48 with 2 non-zero elements.