Tikhonov regularization is the most popular general-purpose method for regularization, a mathematical technique to suppress the effect of noise in data, and uses much of the machinery of Hilbert space theory. This book develops the theory of Tikhonov regularization for a certain class of linear inverse problems which are defined on Hilbert spaces. To explain why and how Tikhonov regularization works, the singular value expansion for compact operators is introduced. Tikhonov regularization with seminorms is also analyzed and for this purpose, densely defined unbounded operators are addressed and their basic properties presented. In addition, the author provides readers with a quick but thorough review of Hilbert space theory and a brief introduction to weak derivatives and Sobolev spaces. Intended as an expository work for those interested in inverse problems and Tikhonov regularization, including graduates and researchers, the author presents the theory in an engaging and straightforward style.
| ISBN: | 9780883851418 |
| Publication date: | 30th December 2016 |
| Author: | Mark S Gockenbach |
| Publisher: | Mathematical Association of America an imprint of The Mathematical Association of America |
| Format: | Hardback |
| Pagination: | 336 pages |
| Series: | The Carus Mathematical Monographs |
| Genres: |
Numerical analysis |
Tikhonov regularization is the most popular general-purpose method for regularization, a mathematical technique to suppress the effect of noise in data, and uses much of the machinery of Hilbert space theory. This book develops the theory of Tikhonov regularization for a certain class of linear inverse problems which are defined on Hilbert spaces. To explain why and how Tikhonov regularization works, the singular value expansion for compact operators is introduced. Tikhonov regularization with seminorms is also analyzed and for this purpose, densely defined unbounded operators are addressed and their basic properties presented. In addition, the author provides readers with a quick but thorough review of Hilbert space theory and a brief introduction to weak derivatives and Sobolev spaces. Intended as an expository work for those interested in inverse problems and Tikhonov regularization, including graduates and researchers, the author presents the theory in an engaging and straightforward style.
Linear Inverse Problems and Tikhonov Regularization features in the following genres: Numerical analysis
Linear Inverse Problems and Tikhonov Regularization is available in Hardback
Linear Inverse Problems and Tikhonov Regularization was written by Mark S Gockenbach and published by Mathematical Association of America an imprint of The Mathematical Association of America
Linear Inverse Problems and Tikhonov Regularization has 336 pages
Yes it is part of The Carus Mathematical Monographs series