Proceedings of the KIEE Conference (대한전기학회:학술대회논문집)

The Korean Institute of Electrical Engineers (대한전기학회)
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Efficient Algorithms for Computing Eigenpairs of Hermitian Matrices

Hermitian 행렬의 고유쌍을 계산하는 효율적인 알고리즘

  • Jeon, Chang-Wan (Department of Control and Instrumentation Eng., Seoul Nat'l University, Automatic Control Research Center) ;
  • Kim, Hyung-Jung (Department of Control and Instrumentation Eng., Kwang-won Nat'l University) ;
  • Lee, Jang-Gyu (Department of Control and Instrumentation Eng., Seoul Nat'l University, Automatic Control Research Center)
  • 전창완 (서울대학교 제어계측공학과 자동제어 특화연구센터) ;
  • 김형중 (강원대학교 제어계측공학과) ;
  • 이장규 (서울대학교 제어계측공학과 자동제어 특화연구센터)
  • Published : 1995.07.20
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Abstract

This paper presents a Generalized Iteration (GI) which includes power method, inverse power method, shifted inverse power method, and Rayleigh quotient iteration (RQI), and modified RQI (MRQI). Furthermore, we propose a GI-based algorithm to find arbitrary eigenpairs for Hermitian matrices. The proposed algorithm appears to be much faster and more accurate than the valuable generalized MRQI of Hu (GMRQI-Hu). The idea of GI is also employed to speed up the GMRQI-Hu and we propose a modified version of Hu's GMRQI (GMRQI-Hu-mod) which is improved in the convergence rate. Some numerical simulation results are presented to confirm our contributions

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