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# Study on Eigen Values And Eigen Vectors of Matrices: An Iterative Approach

 dc.contributor.advisor Jamali, Prof. Dr. A. R. M. Jalal Uddin dc.contributor.author Alam, Md. Sah dc.date.accessioned 2018-05-20T10:10:51Z dc.date.available 2018-05-20T10:10:51Z dc.date.copyright 2016 dc.date.issued 2016-05 dc.identifier.other ID 1251552 dc.identifier.uri http://hdl.handle.net/20.500.12228/129 dc.description This thesis is submitted to the Department of Mathematics, Khulna University of Engineering & Technology in partial fulfillment of the requirements for the degree of Master of Philosophy in Mathematics, May 2016. en_US dc.description Cataloged from PDF Version of Thesis. dc.description Includes bibliographical references (pages 70-75). dc.description.abstract There are some smart methods, available in the literature, which are able to find out all Eigen values. But those methods could not find corresponding Eigen vectors simultaneously. Power method and Inverse Power method are able to find out both Eigen-pairs simultaneously. Power method frequently used for finding only largest Eigen value and corresponding Eigen vector. On the other hand Inverse Power method is applied to find out only smallest Eigen value (or desire Eigen value) and corresponding Eigen vector. But Inverse Power method is computationally costly and some time it is unstable for the presence of inverse of the matrix. It is theoretically observed that if all Eigen values are either positive or negative, then without implement of Inverse Power method the modified (using shifting property) Power method is also able to find out smallest Eigen-pair. Here we have proposed Modified Hybrid Iterative Algorithm based on both Power method and Inverse Power method respectively to find out both largest and smallest Eigen-pairs simultaneously. Moreover several lemma regarding the proposed algorithm have been proposed. The proof of each lemma has also been given along with some suitable illustration. Several experiments have been performed to investigate the robustness and effectiveness of the algorithm as well as the lemma. The proposed algorithm is able to find out both (largest and smallest) Eigen-pairs successfully as well as efficiently. en_US dc.description.statementofresponsibility Md. Sah Alam dc.format.extent 75 pages dc.language.iso en_US en_US dc.publisher Khulna University of Engineering & Technology (KUET), Khulna, Bangladesh. en_US dc.rights Khulna University of Engineering & Technology (KUET) thesis/dissertation/internship reports are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. dc.subject Eigen Vectors en_US dc.subject Eigen Values en_US dc.subject Eigen-Pairs en_US dc.title Study on Eigen Values And Eigen Vectors of Matrices: An Iterative Approach en_US dc.type Thesis en_US dc.description.degree Master of Philosophy in Mathematics dc.contributor.department Department of Mathematics
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