Abstract:
A new scheme of an a posteriori accuracy estimate for solutions of linear
ill-posed problems is proposed along with an algorithm of its calculation.
A new notion of an extra-optimal regularizing algorithm is introduced as a
method for solving ill-posed problems with an a posteriori accuracy estimate
optimal in order. An example of an optimal-in-order method being
not extra-optimal is discussed. The developed theory
is illustrated by a numerical experiment.
Keywords:ill-posed problems; regularizing algorithms; a posteriori accuracy estimates; extra-optimal algorithm.
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