Structured Matrix Algorithms for Inverse Scattering on the Line

VAN DER MEE, CORNELIS VICTOR MARIA;SEBASTIANO SEATZU;DANIELA THEIS

2007-01-01

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Abstract

In this article the Marchenko integral equations leading to the solution of the inverse scattering problem for the 1-D Schrödinger 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.