Geophysical Journal | 1999 volume 21 Ή6

On stable methods of solving problems of definition of star - shaped domains similar to the peset ones. 2.

© Chernay O.A.

For the first time, the existence of a regularizing operator is established for a linear equation of the first kind with a non-negative operator which, among its known modifications, has the best conditionality. The operator brings in conformity with each function from the Gilbert's space of data the functions of the Gilbert's space of solutions having a generalized derivative integrated in the second power. In turn, each function calculated by this operator is an extreme of a smoothing functional which is a weighted sum of the functional of the type of discrepancy with one of the proposed stabilizers which provide an unambiguous solubility of the initial problems.

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