Kuramshina, I. Kochikov and A. Thouraya N. Baranger B. Angermann, V. Trofimov, O. Matusevich, I. Shirokov, and M. AP Smirnov et al. Frolov and E. Smirnov, Y. Shestopalov, and E. Samokhina and E.
Klibanov, A new approximate mathematical model for global convergence for a coefficient inverse problem with backscattering data, J. Inverse and Ill-Posed Problems, 20, , Kuzhuget, L. Klibanov, A. Sullivan, L. Nguyen and M. Fiddy, Blind backscattering experimental data collected in the field and an approximately globally convergent inverse algorithm, Inverse Problems, 28, , Klibanov, The philosophy of the approximate global convergence for multidimensional coefficient inverse problems, Complex Variables and Elliptic Equations, 57, , Klibanov, Approximate global convergence and quasi-reversibility for a coefficient inverse problem with backscattering data, J.
Applicable Analysis. Beilina, L. New a posteriori error estimates for adaptivity technique and global convergence for a hyperbolic coefficient inverse problem. Klibanov, M. Why a minimizer of the Tikhonov functional is closer to the exact solution than the first guess.
Journal of Inverse and Ill - Posed Problems. Adaptivity with relaxation for ill-posed problems and global convergence for a coefficient inverse problem. A posteriori error estimates for the adaptivity technique for the Tikhonov functional and global convergence for a coefficient inverse problem. Inverse Problems, 26, Inverse Problems. Synthesis of global convergence and adaptivity for a hyperbolic coefficient inverse problem in 3D. Journal of Inverse and Ill-Posed Problems. Picosecond scale experimental verification of a globally convergent algorithm for a coefficient inverse problem.
Koshev, N. Orlikovsky, E. Rau, A. Solution of the inverse problem of restoring the signals from an electronic microscope in the backscattered electron mode on the class of bounded variation functions.
Korolev, A. Error estimation in linear inverse problems with prior information. A posteriori error estimates for approximate solutions of irregular operator equations. Doklady of Mathematics V. Bocharov, I. Gainova , together with V.
Chereshnev, S. Bazhan, B Bachmetyev, J. Argilaguet, J. Romanov, A two-dimensional inverse problem for the viscoelasticity equation, Siberian Mathematical Journal, Vol. Romanov, A. Nazarov, Uniqueness theorem in inverse problem of integral-differential equation in electrodynamics, Siberian Journal of Industrial Mathematics, V.
Approximate Global Convergence and Adaptivity for Coefficient Inverse Problems - Semantic Scholar
Shestopalov, Y. This kind of inverse problem gained a lot of interest over the last years because several applications and constraints are formulated quite naturally in a Banach space framework: sparsity, uniform and impulsive noise, preserving discontinuities edges etc. In parameter identification tasks, for instance, the searched-for parameter often appears in the governing partial differential equations as an -coefficient, e.
There you will find the tutorial assignments as well as supplemental material. The book by Beilina and the two books by Scherzer et al. The PhD thesis of Margotti is freely available. Just follow the links from above. Department of Mathematics. Event Calendar. The main topic of the course is to solve nonlinear ill-posed problems where operates between the Banach spaces and with domain of definition.
Knowledge of Functional Analysis and of some basics in Inverse Problems are advantageous.
Beilina, M. Kaltenbacher, A.
SIAM Journal on Scientific Computing
Neubauer, O. Scherzer: Iterative regularization methods for nonlinear ill-posed problems, de Gruyter, F. Scherzer ed.