Geodesic
Necessary and sufficient conditions for the polynomial convergence of the quasi-reversibility and finite-difference methods for an ill-posed Cauchy problem with exact data
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 12, pp. 2027-2041

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The convergence of the quasi-reversibility method and two classes of finite-difference methods for solving the ill-posed Cauchy problem for the first-order equation with a sectorial operator in a Banach space is analyzed. The necessary and sufficient conditions — close to one another — for the convergence of these methods with a rate polynomial with respect to the regularization parameter or discretization step are obtained in terms of the exponent in the source representability of the solution. 
@article{ZVMMF_2015_55_12_a5,
     author = {M. M. Kokurin},
     title = {Necessary and sufficient conditions for the polynomial convergence of the quasi-reversibility and finite-difference methods for an ill-posed {Cauchy} problem with exact data},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {2027--2041},
     publisher = {mathdoc},
     volume = {55},
     number = {12},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_12_a5/}
}
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M. M. Kokurin. Necessary and sufficient conditions for the polynomial convergence of the quasi-reversibility and finite-difference methods for an ill-posed Cauchy problem with exact data. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 12, pp. 2027-2041. http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_12_a5/