Abstract
This paper is an exposition of the basic theory of regularization for an ill-posed linear operator equation subject to a linear operator constraint. The ordinary theory of regularization is subsumed as a special case. The theory is developed by changing the geometric structure of the underlying Hilbert space and invoking well known results on generalized inverses. In addition to the basic theory, the convergence of an approximation method, including a finite element implementation, is considered.
Keywords
- Linear Operator
- Generalize Inverse
- Tikhonov Regularization
- Fredholm Integral Equation
- Unbounded Operator
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Partially supported by a grant from the National Science Foundation.
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© 1986 Springer-Verlag Berlin Heidelberg
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Groetsch, C.W. (1986). Regularization with linear equality constraints. In: Talenti, G. (eds) Inverse Problems. Lecture Notes in Mathematics, vol 1225. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0072663
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DOI: https://doi.org/10.1007/BFb0072663
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-17193-5
Online ISBN: 978-3-540-47353-4
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