Optimal Methods for Ill-Posed Problems
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Vitalii P. Tanana
About this book
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
- A compact and up-to-date overview of optimal methods for solving ill-posed problems
- Covers error estimates and applications to heat conduction problems
- Of interest to reseachers and graduate students in applied mathematics and engineering
Author / Editor information
Reviews
"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
Topics
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Frontmatter
I -
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Introduction
V -
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Contents
VII -
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1. Modulus of continuity of the inverse operator and methods for solving ill-posed problems
1 -
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2. Lavrent’ev methods for constructing approximate solutions of linear operator equations of the first kind
15 -
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3. Tikhonov regularization method
31 -
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4. Projection-regularization method
65 -
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5. Inverse heat exchange problems
77 -
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References
123 -
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Index
129
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