Geodesic
On possibility of obtaining linear accuracy evaluation of approximate solutions to inverse problems
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2016), pp. 29-35

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We consider a concept of linear a priori estimate of the accuracy for approximate solutions to inverse problems with perturbed data. We establish that if the linear estimate is valid for a method of solving the inverse problem, then the inverse problem is well-posed according to Tikhonov. We also find conditions, which ensure the converse for the method of solving the inverse problem independent on the error levels of data. This method is well-known method of quasi-solutions by V. K. Ivanov. It provides for well-posed (according to Tikhonov) inverse problems the existence of linear estimates. If the error levels of data are known, a method of solving well-posed according to Tikhonov inverse problems is proposed. This method called the residual method on the correctness set (RMCS) ensures linear estimates for approximate solutions. We give an algorithm for finding linear estimates in the RMCS.
Keywords: inverse problems, linear a priori estimate of the accuracy, well-posedness according to Tikhonov. 
@article{IVM_2016_10_a3,
     author = {A. S. Leonov},
     title = {On possibility of obtaining linear accuracy evaluation of approximate solutions to inverse problems},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {29--35},
     publisher = {mathdoc},
     number = {10},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2016_10_a3/}
}
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A. S. Leonov. On possibility of obtaining linear accuracy evaluation of approximate solutions to inverse problems. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2016), pp. 29-35. http://geodesic.mathdoc.fr/item/IVM_2016_10_a3/