A parameter choice for Tikhonov regularization for solving nonlinear inverse problems leading to optimal convergence rates
Applications of Mathematics (1993)
- Volume: 38, Issue: 6, page 479-487
- ISSN: 0862-7940
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topScherzer, Otmar. "A parameter choice for Tikhonov regularization for solving nonlinear inverse problems leading to optimal convergence rates." Applications of Mathematics 38.6 (1993): 479-487. <http://eudml.org/doc/15768>.
@article{Scherzer1993,
abstract = {We give a derivation of an a-posteriori strategy for choosing the regularization parameter in Tikhonov regularization for solving nonlinear ill-posed problems, which leads to optimal convergence rates. This strategy requires a special stability estimate for the regularized solutions. A new proof fot this stability estimate is given.},
author = {Scherzer, Otmar},
journal = {Applications of Mathematics},
keywords = {nonlinear inverse problems; parameter choice strategy; nonlinear ill- posed problems; Hilbert spaces; Tikhonov regularization; convergence rate; numerical examples; nonlinear inverse problems; parameter choice strategy; nonlinear ill- posed problems; Hilbert spaces; Tikhonov regularization; convergence rate; numerical examples},
language = {eng},
number = {6},
pages = {479-487},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A parameter choice for Tikhonov regularization for solving nonlinear inverse problems leading to optimal convergence rates},
url = {http://eudml.org/doc/15768},
volume = {38},
year = {1993},
}
TY - JOUR
AU - Scherzer, Otmar
TI - A parameter choice for Tikhonov regularization for solving nonlinear inverse problems leading to optimal convergence rates
JO - Applications of Mathematics
PY - 1993
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 38
IS - 6
SP - 479
EP - 487
AB - We give a derivation of an a-posteriori strategy for choosing the regularization parameter in Tikhonov regularization for solving nonlinear ill-posed problems, which leads to optimal convergence rates. This strategy requires a special stability estimate for the regularized solutions. A new proof fot this stability estimate is given.
LA - eng
KW - nonlinear inverse problems; parameter choice strategy; nonlinear ill- posed problems; Hilbert spaces; Tikhonov regularization; convergence rate; numerical examples; nonlinear inverse problems; parameter choice strategy; nonlinear ill- posed problems; Hilbert spaces; Tikhonov regularization; convergence rate; numerical examples
UR - http://eudml.org/doc/15768
ER -
References
top- H. W. Engl H. Gfrerer, 10.1016/0168-9274(88)90017-7, Appl. Num. Math. 4 (1988), 395-417. (1988) MR0948506DOI10.1016/0168-9274(88)90017-7
- H. W. Engl K. Kunisch A. Neubauer, Convergence rates for Tikhonov regularization of nonlinears ill-posed problems, Inverse Problems 5 (1989), 523-540. (1989) MR1009037
- H. Gfrerer, 10.1090/S0025-5718-1987-0906185-4, Mathematics of Computation 49 (1987), 507-522. (1987) Zbl0631.65057MR0906185DOI10.1090/S0025-5718-1987-0906185-4
- C. W. Groetsch, The Theory of Tikhonov Regularization for Fredholm Equations of the First Kind, Pitman, Boston, 1984. (1984) Zbl0545.65034MR0742928
- A. Neubauer, Tikhonov regularization for non-linear ill-posed problems: optimal convergence rates and finite-dimensional approximation, Inverse Problems 5 (1989), 541-557. (1989) MR1009038
- O. Scherzer H. W. Engl K. Kunisch, Optimal a-posteriori parameter choice for Tikhonov regularization for solving nonlinear ill-posed problems, SIAM J. on Numer. Anal., to appear. MR1249043
- T. L Seidman C. R. Vogel, Well-posedness and convergence of some regularization methods for nonlinear ill-posed problems, Inverse Problems 5 (1989), 227-238. (1989) MR0991919
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