Study on Eigen Values and Eigen Vectors of Matrices : An Iterative Approach

  • ARM Jalal Uddin Jamali Department of Mathematics, Khulna University of Engineering and Technology (KUET), Khulna
  • Md Hasibul Haque Department of Mathematics, Khulna University of Engineering and Technology (KUET), Khulna
  • Md Sah Alam Department of Mathematics, Khulna University of Engineering and Technology (KUET), Khulna
Keywords: Eigen value, Eigen vector, Power method, Inverse Power method, Iterative method, Modified Hybrid Iterative Algorithm

Abstract

Power method is frequently used for finding largest Eigen-pair. On the other hand, Inverse Power method is utilized to find smallest Eigen-pair. Using shifting property, Power method and/or Inverse Power method can be used to find out other desired Eigen pairs too. Several lemmas based on Power method with shifting property are presented here. Moreover, a Modified Hybrid Iterative Algorithm based upon both Power method and Inverse Power method is proposed to find both largest and smallest Eigen-pairs simultaneously with ease. Several experiments have been performed to investigate the robustness and effectiveness of the algorithm. The proposed algorithm is able to find both (largest and smallest) Eigen-pairs successfully and efficiently. Moreover, the proposed algorithm is able to find out the nature (positive and negative sign) of the Eigen values and in some cases the algorithm is also able to find out the second largest Eigen pair in consequence.

GANIT J. Bangladesh Math. Soc.Vol. 37 (2017) 51-61

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Abstract
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PDF
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Published
2018-02-20
How to Cite
Jamali, A. J., Haque, M. H., & Alam, M. S. (2018). Study on Eigen Values and Eigen Vectors of Matrices : An Iterative Approach. GANIT: Journal of Bangladesh Mathematical Society, 37, 51-61. https://doi.org/10.3329/ganit.v37i0.35725
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Articles