Since the inversion of Equation 5 is ill-posed, the equation cannot be directly solved for g and it is necessary to stabilize the problem numerically . One possibility is a regularization approach, which uses a justified bias as an additional selection criterion among the many possible solutions according to their physical plausibility. This bias is chosen in a way that extreme or unphysical features of the DRT, such as spikes, steep slopes, or extreme oscillations of the distribution, are penalized. The penalty or constraint may be chosen such that certain features can still occur, but only if justified by the data as an increase in fit quality that is not just overfitting of noise. The regularization algorithm should favor the solution with the broadest distribution of lines that is still consistent with the data, hence line broadening beyond the underlying distribution of time constants corresponds to the uncertainty of the fit due to experimental noise. The inversion of Equation 5 can be formulated as a minimization problem where g is estimated through the numerical calculation of the Tikhonov regularization in generalized form, ĝ = min