Tikhonovs regularization method for ill-posed problems

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Abstract

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.