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Non-Krylov Non-iterative Subspace Methods For Linear Discrete Ill-posed Problems

Bai, Xianglan
http://orcid.org/0000-0003-0318-6202
http://rave.ohiolink.edu/etdc/view?acc_num=kent1627042947894919

Abstract Details

2021, PHD, Kent State University, College of Arts and Sciences / Department of Mathematical Sciences.
To solve an ill-posed linear discrete inverse problem, we usually solve a nearby penalized (or regularized) problem instead, and when such regularized problem has a large scale, a iterative method based on Krylov subspace is usually the first choice. But these Krylov methods generate solution subspace sequentially and only one new solution subspace basis vector is computed at a time. Therefore it can be difficult to take advantage of multiprocessor or parallel computing. In this thesis we look into the potential of a certain type of non-iterative non-krylov methods which update its solution subspace with a “block”. First, in Chapter 2 we compare the performance of a classic Krylov method based on Golub-Kahan bidiagonalization with a randomized method on a Tikhonov regularized problem and discusses characteristics of linear discrete ill-posed problems that suited for solution by a randomized method. Then in Chapter 3 with the help of a randomized singular value decomposition(RSVD) method to approximate the singular value decomposition(SVD) of a large matrix A, we can therefore apply truncated singular value decomposition(TSVD) regularization method or modified TSVD method, where it is usually not feasible due to efficiency consideration. We also discussed possible remedy for situations when a linear discrete ill-posed problem doesn’t present a randomized method favoring characteristics. And at last, in Chapter 4 we propose another non-iterative non-Krylov method based on discretized Chebyshev polynomials, which is competitive in experiments compared to a Krylov method and a randomized method.
Lothar Reichel (Committee Chair)
Alessandro Buccini (Committee Co-Chair)
Jing Li (Committee Member)
Jun Li (Committee Member)
Hassan Peyravi (Committee Member)
Mikhail Nesterenko (Committee Member)
102 p.
Applied Mathematics
inverse problems, ill-posed problems, singular values, randomized method, Chebyshev expansion method, Krylov subspace, Krylov methods

Recommended Citations

Citations

  • Bai, X. (2021). Non-Krylov Non-iterative Subspace Methods For Linear Discrete Ill-posed Problems [Doctoral dissertation, Kent State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=kent1627042947894919

    APA Style (7th edition)

  • Bai, Xianglan. Non-Krylov Non-iterative Subspace Methods For Linear Discrete Ill-posed Problems. 2021. Kent State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=kent1627042947894919.

    MLA Style (8th edition)

  • Bai, Xianglan. "Non-Krylov Non-iterative Subspace Methods For Linear Discrete Ill-posed Problems." Doctoral dissertation, Kent State University, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=kent1627042947894919

    Chicago Manual of Style (17th edition)

kent1627042947894919
412
© 2021, some rights reserved.Creative Commons License Non-Krylov Non-iterative Subspace Methods For Linear Discrete Ill-posed Problems by Xianglan Bai 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.