Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

 

 

On Tikhonov's method for ill-posed problems


Author: Joel N. Franklin
Journal: Math. Comp. 28 (1974), 889-907
MSC: Primary 65R05
MathSciNet review: 0375817
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Abstract: For Tikhonov's regularization of ill-posed linear integral equations, numerical accuracy is estimated by a modulus of convergence, for which upper and lower bounds are obtained. Applications are made to the backward heat equation, to harmonic continuation, and to numerical differentiation.


References [Enhancements On Off] (What's this?)

  • [1] A. N. Tihonov, On the solution of ill-posed problems and the method of regularization, Dokl. Akad. Nauk SSSR 151 (1963), 501–504 (Russian). MR 0162377
  • [2] A. N. Tihonov, On the regularization of ill-posed problems, Dokl. Akad. Nauk SSSR 153 (1963), 49–52 (Russian). MR 0162378
  • [3] Jane Cullum, Numerical differentiation and regularization, SIAM J. Numer. Anal. 8 (1971), 254–265. MR 0290567
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  • [5] Fritz John, Continuous dependence on data for solutions of partial differential equations with a presribed bound, Comm. Pure Appl. Math. 13 (1960), 551–585. MR 0130456

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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1974-0375817-5
Keywords: Ill-posed, improperly posed, regularization, Tikhonov's method, backward heat equation, harmonic continuation, numerical differentiation
Article copyright: © Copyright 1974 American Mathematical Society