Abstract
Throughout this paper, let X and Y be real Hilbert spaces, T be a bounded linear operator on X into Y, y e Y. We look for the “best-approximate solution” of (1.1) Tx = y, i.e., the unique element that has minimal norm among all minimizers of the residual |Tx-y|. The best-approximate solution is actually given by T†y where T is the Moore-Penrose generalized inverse of T (see e.g. [15], [7]).
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Engl, H.W., Neubauer, A. (1985). Optimal Discrepancy Principles for the Tikh0n0v Regularization of Integral Equations of the First Kind. In: Hämmerlin, G., Hoffmann, KH. (eds) Constructive Methods for the Practical Treatment of Integral Equations. International Series of Numerical Mathematics, vol 73. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-9317-6_10
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DOI: https://doi.org/10.1007/978-3-0348-9317-6_10
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