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Bruckner, Gottfried [VerfasserIn]; Yamamoto, Masahiro [VerfasserIn]

On an operator equation with noise in the operator and the right-hand side with application to an inverse vibration problem

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  • Medientyp: E-Book; Bericht; Sonstige Veröffentlichung
  • Titel: On an operator equation with noise in the operator and the right-hand side with application to an inverse vibration problem
  • Beteiligte: Bruckner, Gottfried [VerfasserIn]; Yamamoto, Masahiro [VerfasserIn]
  • Erschienen: Weierstrass Institute for Applied Analysis and Stochastics publication server, 1998
  • Sprache: Englisch
  • DOI: https://doi.org/10.20347/WIAS.PREPRINT.407
  • Schlagwörter: 35L05 ; 35R30 ; regularization -- linear operator equation -- uncertain operator -- noisy right-hand side -- wave equation -- point source reconstruction ; 65J20 ; article
  • Entstehung:
  • Anmerkungen: Diese Datenquelle enthält auch Bestandsnachweise, die nicht zu einem Volltext führen.
  • Beschreibung: 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, and in both the cases the ill-posedness can be characterized by an embedding operator. 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.