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- Title
STUDY ON EIGEN VALUES AND EIGEN VECTORS OF MATRICES : AN ITERATIVE APPROACH.
- Authors
Jamali, A. R. M. Jalal Uddin; Haque, Md. Hasibul; Alam, Md. Sah
- 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.
- Subjects
EIGENVALUES; ITERATIVE methods (Mathematics); ALGORITHMS; MATRICES (Mathematics); MATHEMATICAL models
- Publication
Ganit: Journal of Bangladesh Mathematical Society, 2017, Issue 37, p51
- ISSN
1606-3694
- Publication type
Article