Stability of the solutions to 3D inverse scattering problems with fixed-energy data. Abstract A review of the author's results is given. Inversion formulas and stability results for the solutions to 3D inverse scattering problems with fixed energy data are obtained. Inversion of exact and noisy data is considered. The inverse potential scattering problem with fixed-energy scattering data is dis...

A review of the author’s results is given. Inversion formulas and stability results for the solutions to 3D inverse scattering problems with fixed energy data are obtained. Inversion of exact and noisy data is considered. The inverse potential scattering problem with fixed-energy scattering data is discussed in detail, inversion formulas for the exact and for noisy data are derived, error estim...

In the present work, under some di¤erentiability conditions on the potential functions , we …rst reduce the inverse scattering problem (ISP) for the polynomial pencil of the Scroedinger equation to the corresponding ISP for the generalized matrix Scrödinger equation . Then ISP will be solved in analogy of the Marchenko method. We aim to establish an e¤ective algorithm for uniquely reconstructin...