A Regularised Total Least Squares Approach for 1D Inverse Scattering
نویسندگان
چکیده
We study the inverse scattering problem for a Schrödinger operator related to static wave with variable velocity, using GLM (Gelfand–Levitan–Marchenko) integral equation. assume have noisy data, and we derive stability estimate error of solution equation by showing invertibility between suitable function spaces. To regularise problem, formulate variational total least squares show that, under certain regularity assumptions, optimisation admits minimisers. Finally, compute numerically regularised method in discrete sense.
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ژورنال
عنوان ژورنال: Mathematics
سال: 2022
ISSN: ['2227-7390']
DOI: https://doi.org/10.3390/math10020216