Let be a linear, closed, and densely defined unbounded operator, where X and Y are Hilbert spaces. Assume that A is not boundedly invertible. Suppose the equation
References
[1]
Tikhonov, A.N. and Arsenin, V.Ya. (1978) Solution of Ill-Posed Problems. John Wiley & Sons, Hoboken.
Bakushinsky, A. and Goncharsky, A. (1994) Ill-Posed Problems: Theory and Applications. Springer, Berlin. https://doi.org/10.1007/978-94-011-1026-6
[4]
Engl, H.W., Hanke, M. and Neubauer, A. (2000) Regularization of Inverse Problems. Kluwer, Alphen aan den.
[5]
Morozov, V.A. (1984) Methods for Solving Incorrectly Posed Problems. Springer-Verlag, New York. https://doi.org/10.1007/978-1-4612-5280-1
[6]
Ramm, A.G. (2005) Inverse Problems. Springer-Verlag, New York.
[7]
Ramm, A.G. (2007) Ill-Posed Problems with Unbounded Operators. Journal of Mathematical Analysis and Applications, 325, 490-495. https://doi.org/10.1016/j.jmaa.2006.02.004
[8]
Van Kinh, N., Chuong, N.M. and Gorenflo, R. (1996) Regularization Method for Nonlinear Variational Inequalities. Proceedings of the First National Workshop “Optimization and Control”, Quinhon, May 27 - June 1, 1996, 53-64. (Preprint: Nr. A-89-28, Freie Universitat, Berlin).
[9]
Van Kinh, N. (2007) Lavrentiev Regularization Method for Nonlinear Ill-Posed Problems. Quy Nhon Uni. Journal of Science, No. 1, 13-28.
[10]
Van Kinh, N. (2014) On the Stable Method of Computing Values of Unbounded Operators. Journal Science of Ho Chi MInh City University of Food Industry, No. 2, 21-30.
[11]
Van Kinh, N. (2020) On the Stable Method Computing Values of Unbounded Operators. Open Journal of Optimization, 9, 129-137. https://doi.org/10.4236/ojop.2020.94009
[12]
Zwart, K. (2018) The Spectral Theorem for Unbounded Self-Adjoint Operators and Nelson’s Theorem. Bachelor Thesis, Universiteit Utrecht, Utrecht.
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be a linear, closed, and densely defined unbounded operator, where X and Y are Hilbert spaces. Assume that A is not boundedly invertible. Suppose the equation
