• 충청수학회지
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• 제14권2호
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• pp.55-66
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• 2001

A new stability analysis of QR factorizations using the two types of Householder reflections is presented. It shows that the use of the common type(the first) in QR factorizations with pivoting for size by row and column exchanges leas to rowwise more stability, although the second type has been used in Householder transformation for the better purpose. A row-oriented backward error bound for the second type Householder QR factorizations with column pivoting is drived.

• 한국정보처리학회논문지
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• 제5권4호
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• pp.959-966
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• 1998

본 논문에서 $m{\times}n\;(m{\geq}n)$ 인 토플리즈 행렬의 빠른 QR 인수분해 알고리즘들을 제안한다. 본 알고리즘들은 위치가 변환되어도 불변하는 (shift-invariance) 토플리즈 행렬의 특성을 효과적으로 이용하였다. 알고리즘들의 주요 변환 도구로 안정된 하우스홀더 변환과 하이퍼볼릭 하우스홀더 변환을 사용하였다. 본 알고리즘들은 O(mn)의 연산을 필요로하며, 분산메모리 병렬 컴퓨터에서 쉽게 구현될 수 있다.

• Journal of applied mathematics & informatics
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• 제26권3_4호
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• pp.779-784
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• 2008

We show that $\mathbb{Z}[\sqrt{-p}]$ is not a unique factorization domain (UFD) but a factorization domain (FD) with a condition $1\;+\;a^2p\;=\;qr$, where a and p are positive integers and q and r are positive primes in $\mathbb{Z}$ with q < p. Using this result, we also construct several specific non-unique factorization domains which are factorization domains. Furthermore, we prove that an integral domain $\mathbb{Z}[\sqrt{-p}]$ is not a UFD but a FD for some positive integer p.

• 한국전자통신학회논문지
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• 제17권2호
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• pp.367-374
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• 2022

그래프 노드상에서 발생하는 그래프 신호의 일부를 선택해서 만든 샘플링 신호로부터 원신호를 복원하기 위해, 복원오차를 최소화하기 위한 최적의 샘플링 집합을 선택하는 알고리즘에 관해 연구한다. 복잡도 개선을 위해 복원오차를 직접적으로 최소화하는 대신에, 복원오차의 상한값을 비용함수로 사용하고, QR분해 적용을 통해 발생하는 상삼각행렬의 대각선상에 위치하는 값으로 샘플링을 결정할 수 있게 하는, 저 복잡도를 갖는 반복적 탐욕알고리즘을 제안한다. 기존의 샘플링 선택 방법과 비교하여, 제안 알고리즘이 복원 성능 저하를 평균 5%미만으로 유지하면서, 약 3.5배 빠른 실행시간을 보임을 다양한 그래프 상황에서 실험을 통해 확인한다.

• 한국정보기술응용학회:학술대회논문집
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• 한국정보기술응용학회 2005년도 6th 2005 International Conference on Computers, Communications and System
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• pp.13-16
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• 2005

It would be desirable to have methods for specific problems, which have low communication costs compared to the computation costs, and in specific applications, algorithms need to be developed and mapped onto parallel computer architectures. Main memory access for shared memory system or global communication in message passing system deteriorate the computation speed. In this paper, it is found that the m-step generalization of the block Lanczos method enhances parallel properties by forming m simultaneous search direction vector blocks. QR factorization, which lowers the speed on parallel computers, is not necessary in the m-step block Lanczos method. The m-step method has the minimized synchronization points, which resulted in the minimized global communications compared to the standard methods.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1999년도 제14차 학술회의논문집
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• pp.121-124
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• 1999

Subspace-based state space system identification (4SID) methods have been demonstrated to per-form well in a number of applications, but the properties of these have not been fully analyzed or understood yet. For applying the methods, no assumptions on structure of realization are needed and any coordinate transformation is allowed for the estimates. This is one reason why many kinds of properties expected for identification procedures have not been clarified yet. We illustrate, by using Schur complement, an interpretation of the R matrix yielded by the QR factorization in the 4SID procedure. The results in this paper can be useful for analysis of properties of parameters obtained by 4SID methods.

• 한국산업정보학회논문지
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• 제11권5호
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• pp.163-169
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• 2006

In order to use parallel computers in specific applications, algorithms need to be developed and mapped onto parallel computer architectures. Main memory access for shared memory system or global communication in message passing system deteriorate the computation speed. In this paper, it is found that the m-step generalization of the block Lanczos method enhances parallel properties by forming in simultaneous search direction vector blocks. QR factorization, which lowers the speed on parallel computers, is not necessary in the m-step block Lanczos method. The m-step method has the minimized synchronization points, which resulted in the minimized global communications and main memory access compared to the standard methods.

• 한국정보통신학회논문지
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• 제27권1호
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• pp.103-108
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• 2023

센서 네트워크에서 평균 추정성능을 높이기 위한 저 복잡도를 갖는 센서 노드 선택 알고리즘에 대해 연구한다. 복잡도를 줄이기 위해 직접적인 비용함수인 평균 추정오차를 최소화 하는 대신, 평균 추정오차 공분산 역행렬의 로그행렬식을 비용함수로 채택하고 이를 최대화하는 센서 노드 집합을 선택하기 위한 탐욕적 반복 알고리즘을 제안한다. 비용함수에 있는 관측행렬에 QR분해를 적용하여 단계마다 한 개의 노드를 선택하기 위한 저 복잡도를 갖는 수학적관계식을 유도한다. 다양한 실험을 통해, 추정성능 및 복잡도면에서 기존의 센서 노드 선택기술 대비 제안 알고리즘이 경쟁력있는 성능을 보임을 입증하고 실용적 센서 노드 선택기술로써 다양한 네트워크시스템에 적용할 수 있는 대안을 제시한다.

• Journal of Electrical Engineering and Technology
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• 제2권4호
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• pp.428-433
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• 2007

This paper describes the new eigenvalue algorithm exploiting the Implicit Restarted Arnoldi Method (IRAM) and its application to power systems. IRAM is a technique for combining the implicitly shifted mechanism with a k-step Arnoldi factorization to obtain a truncated form of the implicitly shifted QR iteration. The numerical difficulties and storage problems normally associated with the Arnoldi process are avoided. Two power systems, one of which has 36 state variables and the other 150 state variables, have been tested using the ARPACK program, which uses IRAM, and the eigenvalue results are compared with the results obtained from the conventional QR method.

• Journal of information and communication convergence engineering
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• 제6권3호
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• pp.261-265
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• 2008

This work presents a simplified efficient blind detection algorithm for orthogonal space-time codes(OSTBC). First, the proposed decoder exploits a proper decomposition approach of the upper triangular matrix R, which resulted from Cholesky-factorization of the composition channel matrix, to form an easy-to-solve blind detection equation. Secondly, in order to avoid suffering from the high computational load, the proposed decoder applies a sub-optimal QR-based decoder. Computer simulation results verify that the proposed decoder allows to significantly reduce computational complexity while still satisfying the bit-error-rate(BER) performance.