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On a Noisy Operator Equation and the Identification of Point‐Sources in the 1–D Wave Equation
Author(s) -
Bruckner G.,
Yamamoto M.
Publication year - 2000
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 - 10.1002/1521-4001(200006)80:6<377::aid-zamm377>3.0.co;2-u
Subject(s) - operator (biology) , mathematics , wave equation , mathematical analysis , point (geometry) , integral equation , numerical analysis , geometry , biochemistry , chemistry , repressor , transcription factor , gene
Abstract We consider a linear operator equation with noise in the operator and the right‐hand side. As a concept, the ill‐posedness of the problem is composed of the ill‐posedness with respect to the operator and the ill‐posedness with respect to the right‐hand side. Starting at a numerical procedure for exact data, in the case of noisy data a numerical procedure and error estimates are given. As an example, a Volterra integral equation of the first kind is investigated and finally applied to a point source reconstruction problem for the wave equation. The method is tested by numerical experiments.