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• W4382940211 abstract "This article generalizes the results of the so-called linear functional strategy [R. S. Anderssen, Inverse Problems (Oberwolfach, 1986)], used for fast reconstruction of some particular feature of interest in the solution of a linear inverse problem. Two versions are proposed for nonlinear problems. The first one applies to differentiable forward operators and is based on the One-Step Newton method. The second one, in turn, uses a linearization of the forward operator obtained by the employment of basic Machine Learning techniques, being applicable to non-differentiable operators. As a byproduct of the proposed methods, we derive two variants of the so-called approximate inverse method [A. K. Louis, Inverse Problems, 1996] for nonlinear inverse problems. Numerical tests, using electrical impedance tomography applied to a biphasic flow problem, are presented to test the efficiency of the proposed methods." @default.
• W4382940211 created "2023-07-04" @default.
• W4382940211 creator A5054964073 @default.
• W4382940211 date "2023-07-03" @default.
• W4382940211 modified "2023-09-26" @default.
• W4382940211 title "Linear Functional Strategy and the Approximate Inverse for Nonlinear Ill-Posed Problems" @default.
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• W4382940211 doi "https://doi.org/10.1080/01630563.2023.2227973" @default.
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