A novel approach to estimate the stability of one-dimensional quantum inverse scattering

1998/08/20 by H.J.S. Dorren, Dorren, H. J. S.
Earth and Planetary Sciences · Mathematics · #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical Analysis (math.NA) #Numerical methods in inverse problems #Seismic Imaging and Inversion Techniques #Seismic Waves and Analysis

paper · pdf · doi:10.48550/arxiv.math-ph/9808008

openalex publication_date 1998/08/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present a novel method to estimate the stability of the Marchenko equation for finite data-sets. We show that we can derive a recursion relationship for the Fourier expansion coefficients of the kernel which is solved by the Marchenko equation. The method can easily be implemented numerically. Moreover, we discus the stability of the one-dimensional inverse scattering problem by using Lyapunov exponents. We give conditions on the scattering data to provide stable inversion results. A numerical example is given.

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