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Error Estimations in Linear Inverse Problems With a Priori Information

[+] Author Affiliations
Anatoly G. Yagola, Yury M. Korolev

Lomonosov Moscow State University, Moscow, Russia

Paper No. DETC2011-47799, pp. 457-462; 6 pages
doi:10.1115/DETC2011-47799
From:
  • ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 2: 31st Computers and Information in Engineering Conference, Parts A and B
  • Washington, DC, USA, August 28–31, 2011
  • Conference Sponsors: Design Engineering Division and Computers and Information in Engineering Division
  • ISBN: 978-0-7918-5479-2
  • Copyright © 2011 by ASME

abstract

We consider an inverse problem for an operator equation Az = u. The exact operator A and the exact right-hand side u are unknown. Only their upper and lower estimations are available. We provide techniques of calculating upper and lower estimations for the exact solution belonging to a compact set in this case, as well as a posteriori error estimations. We obtain approximate solutions with an optimal a posteriori error estimate. We also make use of a priori information about the exact solution, e.g. its monotonicity and convexity. The developed software package was applied to solving practical ill-posed problems.

Copyright © 2011 by ASME

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