Abstract
A linear ill-posed problem is considered with a large number of right-hand sides which are known with an identical level of error. A method of solving this problem of the uniform regularization type using averaging functions is considered. The connection between the properties of these functions and the properties of regularizing algorithms is examined. Estimates are obtained of the deviation of the approximate solutions from the averaged accurate solutions, which have the properties of continuous dependence on some parameters of the algorithms.
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