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

  • K. Miller
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 316)


Finite Difference Method Partial Differential Operator Forward Solution Partial Expansion Holomorphic Semigroup 
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  1. [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)MathSciNetCrossRefzbMATHGoogle Scholar
  2. [2]
    Backus, G., Inference from inadequate and inaccurate data, I, Proc. Nat. Acad. Sci. U.S.A., 65 (1970), pp. 1–7.CrossRefzbMATHGoogle Scholar
  3. [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. [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.MathSciNetCrossRefzbMATHGoogle Scholar
  5. [5]
    Lattes, R., and Lions, J., Méthodé de Quasi-Réversibilité et Applications, Dunod, Paris, 1967.zbMATHGoogle Scholar
  6. [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.MathSciNetCrossRefzbMATHGoogle Scholar
  7. [7]
    Miller, K., Least squares methods for ill-posed problems with a prescribed bound, SIAM J. Math. Anal., 1 (1970), pp. 52–73.MathSciNetCrossRefzbMATHGoogle Scholar
  8. [8]
    Miller, K., Stabilized version of the method of quasi-réversibilité, (to appear).Google Scholar
  9. [9]
    Miller, K., Logarithmic convexity results for holomorphic semigroups, (in preparation).Google Scholar
  10. [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. [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.MathSciNetzbMATHGoogle Scholar
  12. [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.MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin 1973

Authors and Affiliations

  • K. Miller
    • 1
  1. 1.Department of MathematicsUniversity of CaliforniaBerkeley

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