Publication Cover
Applicable Analysis
An International Journal
Volume 94, 2015 - Issue 5
62
Views
2
CrossRef citations to date
0
Altmetric
Articles

Linear estimates of accuracy for approximate solutions of inverse problems

Pages 980-990 | Received 18 Feb 2014, Accepted 29 Mar 2014, Published online: 06 May 2014

References

  • Tikhonov AN, Arsenin VY. Solution of ill-posed problems. New York (NY): Wiley; 1977.
  • Vainikko GM, Veretennikov AY. Iterational procedures in ill-posed problems. New York (NY): Wiley; 1985.
  • Bakushinsky AB, Goncharsky AV. Ill-posed problems: theory and applications. Dordrecht: Kluwer Academic Publishers Group; 1994.
  • Engl HW, Hanke M, Neubauer A. Regularization of inverse problems. Dordrecht: Kluwer Academic Publishers; 1996.
  • Bakushinsky AB, Kokurin MYu. Iterative methods for approximate solution of inverse problems. Dordrecht: Springer; 2004.
  • Lavrentiev MM. Some improperly posed problems in mathematical physics. Berlin: Springer; 1967.
  • Ivanov VK, Vasin VV, Tanana VP. The theory of linear Ill-posed problems and its applications. Moscow: Nauka; 1978. Russian.
  • Tanana VP. Methods for solution of nonlinear operator equations. Moscow: Nauka; 1981. Russian.
  • Klibanov MV, Santosa F. A computational quasi-reversibility method for cauchy problems for laplace’s equation. SIAM J. Appl. Math. 1991;51:1653–1675.
  • Tautenhahn U. Optimality for ill-posed problems under general source conditions. Numer. Funct. Anal. Optim. 1998;19:377–398.
  • Nair MT, Pereverzev SV, Tautenhahn U. Regularization in Hilbert scales under general smoothing conditions. Inverse Probl. 2005;21:1851–1869.
  • Vinokurov VA. On the errors of approximate solution of the linear inverse. Soviet Math. Dokl. 1979;246:792–793.
  • Morozov VA. Methods for solving incorrectly posed problems. Berlin: Springer; 1984.
  • Beilina L, Klibanov MV. Approximate global convergence and adaptivity for coefficient inverse problems. New York (NY): Springer; 2012.
  • Tikhonov AN. On the stability of inverse problems. Dokl. USSR Acad. Sci. 1943;39:195–198 . Russian.
  • Tikhonov AN, Goncharsky AV, Stepanov VV, Yagola AG. Numerical methods for the solution of ill-posed problems. Dordrecht: Kluwer Academic Publishers; 1995.
  • Titarenko VN, Yagola AG, Dorofeev KYu, Nikolaeva NN. New approach to error estimation to ill-posed problems with applications to inverse problems of heat conductivity. J. Inverse Ill-Posed Probl. 2002;10:155–170.
  • Dorofeev KYu, Titarenko VN, Yagola AG. Algorithms for constructing a posteriori errors of solutions to ill-posed problems. Comp. Math. Math. Phys. 2003;43:10–23.
  • Nikolaeva NN, Titarenko VN, Yagola AG. Error estimation for solution of Abel equation on sets of monotonic and convex functions. Siberian J. Num. Math. 2003;6:171–180.
  • Edwards RE. Functional analysis. Theory and applications. New York (NY): Holt, Rinehart and Winston; 1965.
  • Leonov AS. Can an a priori error estimate for an approximate solution of an ill-posed problem be comparable with the error in data? Comput. Math. Math. Phys. 2014;54:575–581.
  • Tikhonov AN, Leonov AS, Yagola AG. Nonlinear ill-posed problems. Vol. 1, 2. London: Chapman and Hall; 1998.
  • Leonov AS. Solution of ill-posed inverse problems. Theory review, practical algorithms and MATLAB demonstrations. Moscow: Librokom; 2010. Russian.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.