Optimal Methods for Ill-Posed Problems

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

Auteur
Vitalii P. Tanana and Anna I. Sidikova, South Ural State University, Russia.

Résumé

"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