An Iterative Computer Algorithm for Generating Line Spectra from Linear Viscoelastic Response Functions

Abstract

This paper examines the reasons for the success of a simple iterative computer algorithm proposed earlier, that is useful in generating line spectra from the experimental response functions commonly used in linear viscoelastic theory. Generating spectra from these response functions is mathematically an ill-posed problem because the inversion of the response function leads to instabilities in the calculations. The paper identifies those regions of the response functions in which experimental and computational rounding errors lead to the instabilities and which are thus responsible for the ill-posedness. It shows that these regions can be excluded from the calculations without impairing the line spectra obtained.