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Generalized Krylov subspace methods with applications

Yu, Xuebo
http://rave.ohiolink.edu/etdc/view?acc_num=kent1401937618

Abstract Details

2014, PHD, Kent State University, College of Arts and Sciences / Department of Mathematical Sciences.
The Tikhonov regularization method is a popular method to solve linear discrete illposed problems. The regularized problems can be solved with the aid of the generalized singular value decomposition (GSVD) when the problem is of small to medium size. This decomposition is not practical to use when the problem is of large size since the computation of the GSVD then is too expensive. The idea is to construct a solution subspace of small size with the aid of a generalized Krylov subspace method and find a solution in the solution subspace as an approximation to the solution in the full space. We refer to this as a reduction method. Several reduction methods for solving large Tikhonov regularization problems have been developed and are discussed in the lliterature. In this work we will add three novel reduction methods to this family. Our methods can give approximate solutions of higher accuracy than the GSVD and, therefore are attractive alternatives to the GSVD also when the matrices are small enough for the latter to be computed. In the context of ε-pseudospectrum computations, we propose a new rational Arnoldi method that is well suited for the situation when the rational functions involved have few distinct poles that are applied in a cyclic fashion.
Lothar Reichel, Dr. (Advisor)
Xiaoyu Zheng, Dr. (Committee Member)
Jing Li, Dr. (Committee Member)
Arden Ruttan, Dr. (Committee Member)
Paul A. Farrell, Dr. (Committee Member)
101 p.
Mathematics
Tikhonov regularization; generalized Krylov method; generalized Golub-Kahan; flexible Arnoldi; ill-posed problem; pseudospectrum; rational Arnoldi

Recommended Citations

Citations

  • Yu, X. (2014). Generalized Krylov subspace methods with applications [Doctoral dissertation, Kent State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=kent1401937618

    APA Style (7th edition)

  • Yu, Xuebo. Generalized Krylov subspace methods with applications. 2014. Kent State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=kent1401937618.

    MLA Style (8th edition)

  • Yu, Xuebo. "Generalized Krylov subspace methods with applications." Doctoral dissertation, Kent State University, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=kent1401937618

    Chicago Manual of Style (17th edition)

kent1401937618
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© 2014, all rights reserved.
This open access ETD is published by Kent State University and OhioLINK.