Geodesic
On linear accuracy estimates of Tikhonov's method
Eurasian journal of mathematical and computer applications, Tome 6 (2018) no. 4, pp. 48-61.

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We investigate the rate of convergence of Tikhonov's scheme for solving irregular nonlinear equations with smooth operators in a Hilbert space in assumption that the derivative of the operator at the solution is normally solvable. With an appropriate a priori and a posteriori coordination of the regularization parameter and the level of errors in input data, we prove that the accuracy estimate is proportional to the error level. Without using the normal solvability condition, we establish similar estimates for the convergence rate in proper subspaces of the symmetrized derivative at the solution and at the current Tikhonov's approximation.
Keywords: irregular operator equation, Hilbert space, normally solvable operator, Tikhonov's scheme, proper subspace, accuracy estimate. 
@article{EJMCA_2018_6_4_a4,
     author = {M. Yu. Kokurin},
     title = {On linear accuracy estimates of {Tikhonov's} method},
     journal = {Eurasian journal of mathematical and computer applications},
     pages = {48--61},
     publisher = {mathdoc},
     volume = {6},
     number = {4},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJMCA_2018_6_4_a4/}
}
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M. Yu. Kokurin. On linear accuracy estimates of Tikhonov's method. Eurasian journal of mathematical and computer applications, Tome 6 (2018) no. 4, pp. 48-61. http://geodesic.mathdoc.fr/item/EJMCA_2018_6_4_a4/