An Iterative Nonlinear Mapping Method for the Relaxation Time Distribution

Abstract

We propose a simple numerical method to calculate the relaxation time distribution, which is not based on the regularization method. This method is as precise as the nonlinear regularization method developed by Honerkamp and Weese⁴⁾, and is simpler in mathematical aspects. Our method is an iterative nonlinear mapping that maps any initial distribution to the set of distribution functions whose element H⁽ⁿ⁾(τ) generates moduli very close to those generated by the exact distribution, and is smooth whenever the initial distribution is smooth. By the mapping, the initial distribution becomes close to the exact distribution within less than 10 iterations. This implies that the iterative nonlinear mapping itself contains the role as the regularization term used in the existing regularization methods, while the mapping is not formulated by constructing a counterpart of the regularization term. In other words, this method is free from parameters such as regularization parameter used in the previous regularization methods. Furthermore, our method needs no constraint to keep the distribution non-negative.