Skip to main content

Stabilized quasi-reversibilite and other nearly-best-possible methods for non-well-posed problems

Part of the Lecture Notes in Mathematics book series (LNM,volume 316)

Keywords

  • Finite Difference Method
  • Partial Differential Operator
  • Forward Solution
  • Partial Expansion
  • Holomorphic Semigroup

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   29.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   39.95
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Agmon, S., and Nirenberg, L., Properties of solutions of ordinary differential equations in Banach space, Comm. Pure Appl. Math., 16 (1963), pp. 121–239. (see p. 136)

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. Backus, G., Inference from inadequate and inaccurate data, I, Proc. Nat. Acad. Sci. U.S.A., 65 (1970), pp. 1–7.

    CrossRef  MATH  Google Scholar 

  3. Douglas, J., A numerical method for analytic continuation, Boundary Problems in Differential Equations, Univ. of Wisconsin Press, Madison, 1960, pp. 179–189.

    Google Scholar 

  4. John, F., Continuous dependence on data for solutions of partial differential equations with a prescribed bound, Comm. Pure Appl. Math., 13 (1960), pp. 551–585.

    CrossRef  MathSciNet  MATH  Google Scholar 

  5. Lattes, R., and Lions, J., Méthodé de Quasi-Réversibilité et Applications, Dunod, Paris, 1967.

    MATH  Google Scholar 

  6. Miller, K., Three circle theorems in partial differential equations and applications to improperly posed problems, Arch. Rational Mech. Anal., 16 (1964), pp. 126–154.

    CrossRef  MathSciNet  MATH  Google Scholar 

  7. Miller, K., Least squares methods for ill-posed problems with a prescribed bound, SIAM J. Math. Anal., 1 (1970), pp. 52–73.

    CrossRef  MathSciNet  MATH  Google Scholar 

  8. Miller, K., Stabilized version of the method of quasi-réversibilité, (to appear).

    Google Scholar 

  9. Miller, K., Logarithmic convexity results for holomorphic semigroups, (in preparation).

    Google Scholar 

  10. Miller, K., and Viano, G., On the necessity of nearly-best-p methods for the analytic continuation of scattering data, (to appear).

    Google Scholar 

  11. Pucci, C., Studio col metodo delle differenze di un problema di Cauchy relativo ad equazioni a derivate parziali del secondo ordine di tipo parabolico, Ann. della Scuola Norm. Sup. di Pisa, Serie III, Vol. VII, Fasc. III–IV (1953), pp. 205–215.

    MathSciNet  MATH  Google Scholar 

  12. Pucci, C., Sui problemi di Cauchy non "ben posti", Atti. Accad. Naz. Lincei Rend. Al. Sci. Fis. Mat. Natur. (8), 18 (1955), pp. 473–477.

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1973 Springer-Verlag Berlin

About this paper

Cite this paper

Miller, K. (1973). Stabilized quasi-reversibilite and other nearly-best-possible methods for non-well-posed problems. In: Knops, R.J. (eds) Symposium on Non-Well-Posed Problems and Logarithmic Convexity. Lecture Notes in Mathematics, vol 316. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0069627

Download citation

  • DOI: https://doi.org/10.1007/BFb0069627

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-06159-5

  • Online ISBN: 978-3-540-38370-3

  • eBook Packages: Springer Book Archive