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On the stability of projection methods for solving incorrectly posed problems

Authors
Journal
USSR Computational Mathematics and Mathematical Physics
0041-5553
Publisher
Elsevier
Publication Date
Volume
15
Issue
1
Identifiers
DOI: 10.1016/0041-5553(75)90131-7

Abstract

Abstract AN OPERATOR equation of the first kind (when incorrectly posed in Hadamard's sense) may be regularized by variational methods (the defect method or Tikhanov's method). To find a regularized family of approximate solutions, the projection method may be used. We state the necessary and sufficient conditions on the operator and finite-dimensional spaces, under which the finite-dimensional approximation are convergent.

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