Weighted Regularization Methods for Ill-Posed Problems
| dc.contributor.advisor | George, Santhosh | |
| dc.contributor.author | Kanagaraj, K. | |
| dc.date.accessioned | 2021-08-19T04:59:02Z | |
| dc.date.available | 2021-08-19T04:59:02Z | |
| dc.date.issued | 2020 | |
| dc.description.abstract | This thesis is devoted for obtaining a stable approximate solution for ill-posed operator equation F x = y: In the second Chapter we consider a non-linear illposed equation F x = y; where F is monotone operator defined on a Hilbert space. Our analysis in Chapter 2 is in the setting of a Hilbert scale. In the rest of the thesis, we studied weighted or fractional regularization method for linear ill-posed equation. Precisely, in Chapter 3 we studied fractional Tikhonov regularization method and in Chapters 4 and 5 we studied fractional Lavrentiv regularization method for the linear ill-posed equation A x = y; where A is a positive self-adjoint operator. Numerical examples are provided to show the reliability and effectiveness of our methods. | en_US |
| dc.identifier.uri | https://idr.nitk.ac.in/handle/123456789/16869 | |
| dc.language.iso | en | en_US |
| dc.publisher | National Institute of Technology Karnataka, Surathkal | en_US |
| dc.subject | Department of Mathematical and Computational Sciences | en_US |
| dc.subject | Ill-Posed Problem | en_US |
| dc.subject | Regularization parameter | en_US |
| dc.subject | Discrepancy principle | en_US |
| dc.subject | Fractional Tikhonov regularization method | en_US |
| dc.subject | Monotone Operator | en_US |
| dc.subject | Lavrentiev Regularization | en_US |
| dc.subject | Hilbert Scales | en_US |
| dc.subject | Adaptive Parameter Choice Strategy | en_US |
| dc.title | Weighted Regularization Methods for Ill-Posed Problems | en_US |
| dc.type | Thesis | en_US |