The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. ex. Some numerals are expressed as "XNUMX".
Copyrights notice
The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. Copyrights notice
최소 고유값과 이에 대응하는 고유벡터를 찾는 방법이 고려됩니다. 활용되는 핵심 절차는 수정된 레일리 지수 반복(MRQI)입니다. 레일리 지수 반복(RQI)의 수렴 속도는 3차입니다. 그러나 불행하게도 RQI가 항상 최소 고유값을 찾는 것은 아닙니다. 본 논문에서는 항상 최소 고유쌍을 찾을 수 있는 새로운 MRQI가 제공된다. MRQI를 기반으로 최소 고유쌍을 찾는 빠른 알고리즘이 제안됩니다. 이 방법은 다음과 같은 특징을 가지고 있습니다. 첫째, 포함 간격을 계산하지 않습니다. 둘째, Toeplitz 행렬뿐만 아니라 Hermitian 행렬에서도 작동합니다. 셋째, 최소 고유값이 두 개 이상인 행렬에서 작동합니다. 넷째, 이 방법의 수치적 오차는 매우 작다. 다섯째, 간단하고 빠른 것이 매력적이다. 이 방법의 수렴 속도는 점근적 3차입니다. MATLAB 시뮬레이션 결과는 이 방법이 다른 방법보다 성능이 뛰어날 수 있음을 보여줍니다. MRQI라는 용어는 이미 사용되었습니다. 여러 MRQI 방법의 차이점이 논의됩니다. MRQI의 수학적 특성을 조사합니다. 본 연구는 신호공간을 효율적으로 확보할 수 있기 때문에 통신을 포함한 신호처리의 다양한 분야에 효과적으로 적용될 수 있다.
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부
Chang Wan JEON, Jang Gyu LEE, "A New MRQI Algorithm to Find Minimum Eigenpairs" in IEICE TRANSACTIONS on Information,
vol. E82-D, no. 6, pp. 1011-1019, June 1999, doi: .
Abstract: A method for locating the minimum eigenvalue and its corresponding eigenvector is considered. The core procedure utilized is the modified Rayleigh quotient iteration (MRQI). The convergence rate of the Rayleigh quotient iteration (RQI) is cubic. However, unfortunately, the RQI may not always locate the minimum eigenvalue. In this paper, a new MRQI that can always locate the minimum eigenpair is given. Based on the MRQI, a fast algorithm to locate minimum eigenpair will be proposed. This method has the following characteristics. First, it does not compute the inclusion interval. Second, it works for any Hermitian matrix as well as Toeplitz matrix. Third, it works on matrices having more than one minimum eigenvalue. Fourth, the numerical error of this method is very small. Fifth, it is attractively simple and fast. The convergence rate of this method is asymptotically cubic. MATLAB simulation results show that this method may outperform other methods. The term MRQI has been already used. Differences in several MRQI methods are discussed. Mathematical properties of the MRQI are investigated. This research can be effectively applied to diverse field of the signal processing including communication, because the signal space can be efficiently obtained.
URL: https://global.ieice.org/en_transactions/information/10.1587/e82-d_6_1011/_p
부
@ARTICLE{e82-d_6_1011,
author={Chang Wan JEON, Jang Gyu LEE, },
journal={IEICE TRANSACTIONS on Information},
title={A New MRQI Algorithm to Find Minimum Eigenpairs},
year={1999},
volume={E82-D},
number={6},
pages={1011-1019},
abstract={A method for locating the minimum eigenvalue and its corresponding eigenvector is considered. The core procedure utilized is the modified Rayleigh quotient iteration (MRQI). The convergence rate of the Rayleigh quotient iteration (RQI) is cubic. However, unfortunately, the RQI may not always locate the minimum eigenvalue. In this paper, a new MRQI that can always locate the minimum eigenpair is given. Based on the MRQI, a fast algorithm to locate minimum eigenpair will be proposed. This method has the following characteristics. First, it does not compute the inclusion interval. Second, it works for any Hermitian matrix as well as Toeplitz matrix. Third, it works on matrices having more than one minimum eigenvalue. Fourth, the numerical error of this method is very small. Fifth, it is attractively simple and fast. The convergence rate of this method is asymptotically cubic. MATLAB simulation results show that this method may outperform other methods. The term MRQI has been already used. Differences in several MRQI methods are discussed. Mathematical properties of the MRQI are investigated. This research can be effectively applied to diverse field of the signal processing including communication, because the signal space can be efficiently obtained.},
keywords={},
doi={},
ISSN={},
month={June},}
부
TY - JOUR
TI - A New MRQI Algorithm to Find Minimum Eigenpairs
T2 - IEICE TRANSACTIONS on Information
SP - 1011
EP - 1019
AU - Chang Wan JEON
AU - Jang Gyu LEE
PY - 1999
DO -
JO - IEICE TRANSACTIONS on Information
SN -
VL - E82-D
IS - 6
JA - IEICE TRANSACTIONS on Information
Y1 - June 1999
AB - A method for locating the minimum eigenvalue and its corresponding eigenvector is considered. The core procedure utilized is the modified Rayleigh quotient iteration (MRQI). The convergence rate of the Rayleigh quotient iteration (RQI) is cubic. However, unfortunately, the RQI may not always locate the minimum eigenvalue. In this paper, a new MRQI that can always locate the minimum eigenpair is given. Based on the MRQI, a fast algorithm to locate minimum eigenpair will be proposed. This method has the following characteristics. First, it does not compute the inclusion interval. Second, it works for any Hermitian matrix as well as Toeplitz matrix. Third, it works on matrices having more than one minimum eigenvalue. Fourth, the numerical error of this method is very small. Fifth, it is attractively simple and fast. The convergence rate of this method is asymptotically cubic. MATLAB simulation results show that this method may outperform other methods. The term MRQI has been already used. Differences in several MRQI methods are discussed. Mathematical properties of the MRQI are investigated. This research can be effectively applied to diverse field of the signal processing including communication, because the signal space can be efficiently obtained.
ER -