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• W2808794230 abstract "When we evaluate the expression $${{varvec{f}}} = A{{varvec{u}}}$$ , where $${{varvec{u}}}$$ and $${{varvec{f}}}$$ are vectors and A is a matrix, we solve a direct or forward problem. Given A we can precisely calculate $${{varvec{f}}}$$ for any $${{varvec{u}}}$$ . The only danger we may anticipate in a computer is the one of over- or underflow, or perhaps loss of precision. Solving a backward or inverse problem is a step in the opposite direction: we either wish to reconstruct $${{varvec{u}}}$$ from $${{varvec{f}}}$$ , knowing A — this is the so-called inverse reconstruction problem — or learn something about A from given $${{varvec{u}}}$$ and $${{varvec{f}}}$$ , which is known as the inverse identification problem because we are identifying the parameters of the underlying “model” — the presumed linear mapping embodied by the matrix A. In either case trouble is brewing: A may not be invertible, and even if it were, it may be ill-conditioned. The difficulties could be compounded by the data $${{varvec{f}}}$$ being noisy, or A depending on $${{varvec{u}}}$$ , introducing nonlinearity." @default.
• W2808794230 created "2018-06-29" @default.
• W2808794230 creator A5064090264 @default.
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• W2808794230 date "2018-01-01" @default.
• W2808794230 modified "2023-10-18" @default.
• W2808794230 title "Inverse and Ill-Posed Problems $$star $$⋆" @default.
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• W2808794230 doi "https://doi.org/10.1007/978-3-319-78619-3_12" @default.
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