Structured matrix algorithms for inverse scattering on the line

• DOI: 10.1007/s10092-007-0129-9
• Publication Date: 2007-09-17T14:47:29Z
• Authors: Cornelis van der Mee; Sebastiano Seatzu; Daniela Theis
• Keywords: Matrix (chemical analysis); Theory of computation

In this article the Marchenko integral equations leading to the solution of the inverse scattering problem for the 1-D Schrodinger equation on the line are solved numerically. The linear system obtained by discretization has a structured matrix which allows one to apply FFT based techniques to solve the inverse scattering problem with minimal computational complexity. The numerical results agree with exact solutions when available. A proof of the convergence of the discretization scheme is given. Keywords Structured matrix systems, 1-D inverse scattering, Marchenko integral equation