A discrepancy principle for Tikhonov regularization with approximately specified data

• Autorzy: M. Thamban Nair , Eberhard Schock
• Języki publikacji: EN

Abstrakty

EN

Many discrepancy principles are known for choosing the parameter α in the regularized operator equation $(T*T + αI)x_α^δ = T*y^δ$, $|y - y^δ| ≤ δ$, in order to approximate the minimal norm least-squares solution of the operator equation Tx = y. We consider a class of discrepancy principles for choosing the regularization parameter when T*T and $T*y^δ$ are approximated by Aₙ and $zₙ^δ$ respectively with Aₙ not necessarily self-adjoint. This procedure generalizes the work of Engl and Neubauer (1985), and particular cases of the results are applicable to the regularized projection method as well as to a degenerate kernel method considered by Groetsch (1990).

Słowa kluczowe

EN

ill-posed problems   minimal norm least-squares solution   Moore-Penrose inverse   Tikhonov regularization   discrepancy principle   optimal rate  

Kategorie tematyczne

• 45B05: Fredholm integral equations
• 45E99: None of the above, but in this section
• 65J10: Equations with linear operators (do not use )
• 65R30: Improperly posed problems

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1998
• Tom: 69
• Numer: 3
• Strony: 197-205

Daty

wydano

1998

otrzymano

1995-08-21

poprawiono

1998-05-10

Twórcy

autor

M. Thamban Nair

• Department of Mathematics, Indian Institute of Technology Madras, Chennai 600 036, India

autor

Eberhard Schock

• Fachbereich Mathematik, Universität Kaiserslautern, Kaiserslautern, Germany

Bibliografia

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• [2] H. W. Engl and A. Neubauer, An improved version of Marti's method for solving ill-posed linear integral equations, Math. Comp. 45 (1985), 405-416.
• [3] H. W. Engl and A. Neubauer, Optimal parameter choice for ordinary and iterated Tikhonov regularization, in: Inverse and Ill-Posed Problems, H. W. Engl and C. W. Groetsch (eds.), Academic Press, London, 1987, 97-125.
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