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Regularizaton with closed linear operators. (English) Zbl 0926.47006

Summary: The regularization with closed linear operators is used to solve an operator equation of the first kind. When all initial data are known approximately, we choose the regular parameter by using the general Arcangeli criterion to give the convergence and the asymptotic orders of convergence of the regular solution.

MSC:

47A50 Equations and inequalities involving linear operators, with vector unknowns
47A05 General (adjoints, conjugates, products, inverses, domains, ranges, etc.)
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References:

[1] Chen Chuanzhang, Hou Zongyi, Li Mingzhong, The Theory of Integral Equations and its Applications, Shanghai Scientific and Technical Publishers, Shanghai, 1987 (in Chinese)
[2] Tikhonov A. N., Arsenia V. Ya., Methods of Solving Ill-posed Problems, Nauka, Moscow, 1979 (Russian)
[3] Lavrent’ev M. M., Romonov V. G. and Shishatskii S. P., Ill-posed Problems of Mathematical Physics and Analysis, American Mathematical Society C, 1980
[4] Morozov V. A., Methods for Solving Incorrectly Posed Problems, Springer-Verlag, New York, Berlin, Heidlberg, Tokyo, 1984
[5] Groetsch C. W., The Theory of Tikhonov Regularization for Fredholm Equations of the First Kind, Pitman Advanced Publishing Program, Boston, 1984 · Zbl 0545.65034
[6] Locker J., Prenter P. M., Regularization with differential operators I. general theory, J. Math. Appl., 74: 504–529(1980) · Zbl 0447.65023
[7] Li Henong and Hou Zongyi, Estimate of asymptotics order of Tikhonov regular solution for the operator equation of the first kind with approximate operator and right-hand, Chinese Annals of Mathematics, 14A (3) (1993) (in Chinese) · Zbl 0788.47006
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