Geodesic
On the size of errors in the method of successive approximations
Trudy Instituta matematiki, Tome 21 (2013) no. 2, pp. 91-102.

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A new approach to studying the asymptotic behavior of lengths of vectors-errors in the method of successive approximations for linear operator equations is given. It is shown that for all large enough numbers of iterations the greatest possible errors are the most probable ones. The explicit form for asymptotics of the errors is obtained. 
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P. P. Zabreiko; A. N. Tanyhina. On the size of errors in the method of successive approximations. Trudy Instituta matematiki, Tome 21 (2013) no. 2, pp. 91-102. http://geodesic.mathdoc.fr/item/TIMB_2013_21_2_a5/

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