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On the Error of Approximation of Solutions of Operator Equations by Projective Methods
Author(s) -
Gorbachuk M.
Publication year - 1998
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19980781533
Subject(s) - mathematics , operator (biology) , smoothness , approximation error , mathematical analysis , biochemistry , chemistry , repressor , transcription factor , gene
This paper is devoted to direct and inverse theorems of the approximation theory for solutions of operator equations of the form Au = f. The approximation is realized by variational methods, namely the Ritz method, the method of least squares, and the moment one. It is shown that the error of the approximation by these methods is completely determined by the order of smoothness of a solution with respect to a certain cognate to A operator associated with an approximation method.