Geodesic
Convergence of the Lavrent'ev method
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 6, pp. 958-965

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The convergence of the Lavrent'ev method, which is a well-known regularization method for integral equations of the first kind, is analyzed as applied to equations with arbitrary linear bounded operators. A theorem concerning necessary and sufficient conditions for this convergence is proved. It is shown that these conditions are satisfied for two classes of integral equations that do not possess the properties required by the classical Lavrent'ev method. 
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     author = {G. V. Khromova},
     title = {Convergence of the {Lavrent'ev} method},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {958--965},
     publisher = {mathdoc},
     volume = {49},
     number = {6},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_6_a2/}
}
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G. V. Khromova. Convergence of the Lavrent'ev method. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 6, pp. 958-965. http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_6_a2/