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Modifying Some Iterative Methods for Solving Quadratic Eigenvalue Problems

Ali, Ali Hasan
http://orcid.org/0000-0003-2959-4212
http://rave.ohiolink.edu/etdc/view?acc_num=wright1515029541712239

Abstract Details

2017, Master of Science (MS), Wright State University, Mathematics.
In this thesis, we are investigating the solutions λ of a typical quadratic eigenvalue problem (QEP). Indeed, solutions λ of a QEP of the form Q(λ)=λ2M+λD+S that satisfy Q(λ)=0, can be obtained iteratively and without linearizing the problem. However, many iterative methods can only find some of the solutions λ. Therefore, we are going to modify a method based on Newton iterations in order to find all of the solutions λ, that are known also as the eigenvalues of the QEP. In addition, we will investigate how the proposed method compares with standard iterative methods from the literature. Moreover, we will provide a method for finding an upper bound for the number of the eigenvalues of the QEP, and apply this in our method for the purpose of finding all solutions λ.
Sara Pollock, Ph.D. (Advisor)
Yuqing Chen, Ph.D. (Committee Member)
Weifu Fang, Ph.D. (Committee Member)
66 p.
Applied Mathematics; Mathematics
Quadratic Eigenvalue problem; Matrix Polynomial Problem; Nonlinear Eigenvalue Problem; Newton Iteration; Generalized Eigenvalue Problem; Newton Maehly Method; Newton Maehly Iteration; Newton Correction; QEP; NLEP; NLEVP; MPP; GEP

Recommended Citations

Citations

  • Ali, A. H. (2017). Modifying Some Iterative Methods for Solving Quadratic Eigenvalue Problems [Master's thesis, Wright State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=wright1515029541712239

    APA Style (7th edition)

  • Ali, Ali Hasan. Modifying Some Iterative Methods for Solving Quadratic Eigenvalue Problems. 2017. Wright State University, Master's thesis. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=wright1515029541712239.

    MLA Style (8th edition)

  • Ali, Ali Hasan. "Modifying Some Iterative Methods for Solving Quadratic Eigenvalue Problems." Master's thesis, Wright State University, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=wright1515029541712239

    Chicago Manual of Style (17th edition)

wright1515029541712239
1,280
© 2017, some rights reserved.Creative Commons License Modifying Some Iterative Methods for Solving Quadratic Eigenvalue Problems by Ali Hasan Ali is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License. Based on a work at etd.ohiolink.edu.
This open access ETD is published by Wright State University and OhioLINK.
Release 3.2.12