Optimal Methods for Ill-Posed Problems
Description
The book covers fundamentals of the theory of optimal methods for solving ill-posed problems, as well as ways to obtain accurate and accurate-by-order error estimates for these methods. The methods described in the current book are used to solve a number of inverse problems in mathematical physics.
Contents
Modulus of continuity of the inverse operator and methods for solving ill-posed problems
Lavrent'ev methods for constructing approximate solutions of linear operator equations of the first kind
Tikhonov regularization method
Projection-regularization method
Inverse heat exchange problems
Reviews / Votes
"The book can serve as a course in the corresponding topics for master and PhD students, but it can be also used by researchers working in the eld of inverse problems."
Constantin Popa in: Zentralblatt MATH 1391.65001
"The book is well written and may be used for undergraduate students. The presentation is clear and the proofs are complete."
Antonio C. G. Leitao in: Mathematical Reviews Clippings (April 2019) MR3791504
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Content
- Intro
- Introduction
- Contents
- 1. Modulus of continuity of the inverse operator and methods for solving ill-posed problems
- 2. Lavrent'ev methods for constructing approximate solutions of linear operator equations of the first kind
- 3. Tikhonov regularization method
- 4. Projection-regularization method
- 5. Inverse heat exchange problems
- References
- Index
