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.

**[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****[4]**J. H. Wilkinson,*Rounding errors in algebraic processes*, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1963. MR**0161456****[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