On Tikhonov’s method for ill-posed problems
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- by Joel N. Franklin PDF
- Math. Comp. 28 (1974), 889-907 Request permission
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
- 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
- A. N. Tihonov, On the regularization of ill-posed problems, Dokl. Akad. Nauk SSSR 153 (1963), 49–52 (Russian). MR 0162378
- Jane Cullum, Numerical differentiation and regularization, SIAM J. Numer. Anal. 8 (1971), 254–265. MR 290567, DOI 10.1137/0708026
- J. H. Wilkinson, Rounding errors in algebraic processes, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1963. MR 0161456
- 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 130456, DOI 10.1002/cpa.3160130402
Additional Information
- © Copyright 1974 American Mathematical Society
- Journal: Math. Comp. 28 (1974), 889-907
- MSC: Primary 65R05
- DOI: https://doi.org/10.1090/S0025-5718-1974-0375817-5
- MathSciNet review: 0375817