This article is cited in 14 papers

The critical level of discrepancy in regularization methods

G. M. Vainikko

Tartu

Abstract: A class of methods of solving linear ill-posed problems in Hilbert space is studied. The regularization parameter is chosen from the condition for the norm of the discrepancy to be equal to the level of accuracy in specifying the right-hand side of the equation. This choice of regularization parameter leads in certain cases to a convergent order-wise optimal process, and in others to a divergent process. The case of an approximately specified operator is also considered.

UDC: 517.988.68

MSC: Primary 65J10; Secondary 47A50

Received: 22.02.1982

 English version: USSR Computational Mathematics and Mathematical Physics, 1983, 23:6, 1–9

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