Regularization based on Krylov subspace iterations
| Thesis title in Czech: | Regularizace založená na metodách Krylovových podprostorů |
|---|---|
| Thesis title in English: | Regularization based on Krylov subspace iterations |
| Key words: | ill-posed problémy, regularizace, iterační metody, šum v datech, vyjevování šumu |
| English key words: | ill-posed problems, regularization, iterative methods, noise in the data, noise revealing |
| Academic year of topic announcement: | 2010/2011 |
| Thesis type: | diploma thesis |
| Thesis language: | angličtina |
| Department: | Department of Numerical Mathematics (32-KNM) |
| Supervisor: | doc. RNDr. Iveta Hnětynková, Ph.D. |
| Author: | hidden - assigned and confirmed by the Study Dept. |
| Date of registration: | 11.05.2011 |
| Date of assignment: | 11.05.2011 |
| Confirmed by Study dept. on: | 02.08.2013 |
| Date and time of defence: | 19.09.2013 00:00 |
| Date of electronic submission: | 30.07.2013 |
| Date of submission of printed version: | 02.08.2013 |
| Date of proceeded defence: | 19.09.2013 |
| Opponents: | RNDr. Miloslav Vlasák, Ph.D. |
| Advisors: | prof. Ing. Zdeněk Strakoš, DrSc. |
| Guidelines |
| Krylovovské metody patří mezi populární techniky pro řešení diskrétních ill-posed úloh, s nimiž se můžeme setkat v aplikacích jako je počítačová tomografie, seismologie, astronomie atd. Cílem práce je studium, testování a návrh možných vylepšení metod založených na Krylovovských regularizačních metodách. |
| References |
| P. C. Hansen: Discrete Inverse Problems: Insight and Algorithms, SIAM, 2010.
I. Hnětynková, M. Plešinger, Z. Strakoš: The regularizing effect of the Golub-Kahan iterative bidiagonalization and revealing the noise level in the data, BIT Numerical Mathematics 49, pp. 669-696, 2009. P. C. Hansen, J. G. Nagy, D. P. O´Leary: Deblurring Images: Matrices, Spectra and Filtering, SIAM, 2007. P. C. Hansen: Rank-Deficient and Discrete Ill-Posed Problems - Numerical Aspects of Linear Inversion, SIAM, 1997. |