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Lanczos and Golub-Kahan Reduction Methods Applied to Ill-Posed Problems

Onunwor, Enyinda Nyekachi
http://rave.ohiolink.edu/etdc/view?acc_num=kent1513207378684957

Abstract Details

2018, PHD, Kent State University, College of Arts and Sciences / Department of Mathematical Sciences.
The symmetric Lanczos method is commonly applied to reduce large-scale symmetric linear discrete ill-posed problems to small ones with a symmetric tridiagonal matrix. We investigate how quickly the nonnegative subdiagonal entries of this matrix decay to zero. Their fast decay to zero suggests that there is little benefit in expressing the solution of the discrete ill-posed problems in terms of the eigenvectors of the matrix compared with using a basis of Lanczos vectors, which are cheaper to compute. We will also show that a truncated singular value decomposition, made up of a few of the largest singular values and associated left and right singular vectors, of the matrix of a large-scale linear discrete ill-posed problems can be computed quite inexpensively by an implicitly restarted Golub-Kahan bidiagonalization method. Extensions to hybrid methods for the solution of linear discrete ill-posed problems with several right-hand side vectors will be made. Applications include multi-channel image restoration when the image degradation model is described by a linear system of equations with multiple right-hand sides that are contaminated by errors.
Lothar Reichel, PhD (Advisor)
Li Jing, PhD (Committee Member)
Li Jun, PhD (Committee Member)
Ruttan Arden, PhD (Committee Member)
Bansal Arvind, PhD (Committee Member)
105 p.
Applied Mathematics; Mathematics
Lanczos, Golub-Kahan, SVD, TSVD, Tikhonov, Krylov, Ill-Posed Problems

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Citations

  • Onunwor, E. N. (2018). Lanczos and Golub-Kahan Reduction Methods Applied to Ill-Posed Problems [Doctoral dissertation, Kent State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=kent1513207378684957

    APA Style (7th edition)

  • Onunwor, Enyinda. Lanczos and Golub-Kahan Reduction Methods Applied to Ill-Posed Problems. 2018. Kent State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=kent1513207378684957.

    MLA Style (8th edition)

  • Onunwor, Enyinda. "Lanczos and Golub-Kahan Reduction Methods Applied to Ill-Posed Problems." Doctoral dissertation, Kent State University, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=kent1513207378684957

    Chicago Manual of Style (17th edition)

kent1513207378684957
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© 2018, some rights reserved.Creative Commons License Lanczos and Golub-Kahan Reduction Methods Applied to Ill-Posed Problems by Enyinda Nyekachi Onunwor 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 Kent State University and OhioLINK.