Geodesic
Pointwise extra-optimal regularizing algorithms
Numerical methods and programming, Tome 14 (2013) no. 2, pp. 215-228.

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Pointwise a posteriori accuracy estimates for approximate solutions to multidimensional inverse ill-posed problems, i.e. for functions of several variables, are considered. The estimates are constructed for given values of the argument of an approximate solution found by a regularizing algorithm (RA). A technique for calculation of pointwise a posteriori estimates is proposed. A new notion of a pointwise extra-optimal regularizing algorithm is introduced as a method for the solution of ill-posed problems with a posteriori pointwise accuracy estimate optimal in order for every given argument. A number of examples of pointwise extra-optimal regularizing algorithms are discussed. The proposed theory is illustrated by numerical experiments.
Keywords: ill-posed problems; regularizing algorithms (RA); pointwise a posteriori accuracy estimates; pointwise extra-optimal regularizing algorithms. 
@article{VMP_2013_14_2_a1,
     author = {A. S. Leonov},
     title = {Pointwise extra-optimal regularizing algorithms},
     journal = {Numerical methods and programming},
     pages = {215--228},
     publisher = {mathdoc},
     volume = {14},
     number = {2},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2013_14_2_a1/}
}
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A. S. Leonov. Pointwise extra-optimal regularizing algorithms. Numerical methods and programming, Tome 14 (2013) no. 2, pp. 215-228. http://geodesic.mathdoc.fr/item/VMP_2013_14_2_a1/