Continuum Mechanics and Thermodynamics

, Volume 2, Issue 1, pp 17–30

Tikhonovs regularization method for ill-posed problems

A comparison of different methods for the determination of the regularization parameter
  • J. Honerkamp
  • J. Weese

DOI: 10.1007/BF01170953

Cite this article as:
Honerkamp, J. & Weese, J. Continuum Mech. Thermodyn (1990) 2: 17. doi:10.1007/BF01170953


Frequently the determination of material characteristic functions, such as the molecular mass distribution of a polymeric sample or the relaxation spectrum of a viscoelastic fluid, leads to an ill-posed problem. When Tikhonov regularization is applied to such a problem the problem of an appropriate choice of the regularization parameter arises. Well-known methods to determine this parameter, such as the discrepancy principle, and a method based on the minimization of the predictive mean-square signal error are compared with a self-consistence method. Monte Carlo simulations have been carried out for the determination of the relaxation spectrum from small amplitude oscillatory shear flow data. The self-consistence method has proven to be much more robust and reliable.

Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • J. Honerkamp
    • 1
  • J. Weese
    • 1
  1. 1.Fakultät für PhysikAlbert-Ludwigs-UniversitätFreiburgFRG