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9 papers · 2 filters
Wave scattering by small bodies of arbitrary shapes
A. G. Ramm
In this paper we review the results of the author on the theory of scalar and vector wave scattering by small bodies of an arbitrary shape with the emphasis on practical applicabil…
Application of the hybrid stochastic-deterministic minimization method to a surface data inverse scattering problem
Semion Gutman, Alexander G. Ramm
A method for the identification of small inhomogeneities from a surface data is presented in the framework of an inverse scattering problem for the Helmholtz equation. Using the as…
Stable identification of piecewise-constant potentials from fixed-energy phase shifts
Semion Gutman, Alexander G. Ramm
An identification of a spherically symmetric potential by its phase shifts is an important physical problem. Recent theoretical results assure that such a potential is uniquely def…
Piecewise-constant potentials with practically the same fixed-energy phase shifts
Alexander G. Ramm, Semion Gutman
It has recently been shown that spherically symmetric potentials of finite range are uniquely determined by the part of their phase shifts at a fixed energy level . However,…
A numerical method for solving some nonlinear problems
A. G. Ramm
A nonlinear equation in a Banach space is written as a linear equation with a linear operator depending on the unknown solution. This method, which we call a global linearization m…
Linear ill-posed problems and dynamical systems
Alexander G. Ramm
A linear equation Au=f (1) with a bounded, injective, but not boundedly invertible linear operator in a Hilbert space H is studied. A new approach to solving linear ill-posed probl…