A NEW CONVERGENT ALGORITHM TO APPROXIMATE POTENTIALS FROM FIXED ANGLE SCATTERING DATA

We introduce a new iterative method to recover a real compact supported potential of the Schödinger operator from their fixed angle scattering data. The method combines a fixed point argument with a suitable approximation of the resolvent of the Schödinger operator by partial sums associated to its...

Full description

Saved in:
Bibliographic Details
Published in:SIAM journal on applied mathematics 2018-01, Vol.78 (5), p.2714-2736
Main Authors: BARCELÓ, JUAN A., CASTRO, C., LUQUE, T., VILELA, MARI CRUZ
Format: Article
Language:English
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We introduce a new iterative method to recover a real compact supported potential of the Schödinger operator from their fixed angle scattering data. The method combines a fixed point argument with a suitable approximation of the resolvent of the Schödinger operator by partial sums associated to its Born series. The main interest is that, unlike other iterative methods in the literature, each iteration is explicit (and therefore faster computationally) and a rigorous analytical result on the convergence of the iterations is proved. This result requires potentials with small norm in certain Sobolev spaces. As an application we show some numerical experiments that illustrate this convergence.
ISSN:0036-1399
1095-712X
DOI:10.1137/18M1172247