Tikhonov regularization method

Alvares et. al. [141] successfully applied a method known as the Tikhonov Regularization method and L-curve criterion to generate data in close accord with the Malvern software. 

According to the conventional Tikhonov regularization method, we substitute for the solution of the linear inverse problem (10.16) a minimization of the corresponding parametric functional with, for example, a minimum norm stabilizer ... 

Our goal is to find the parameters inverse problem. The inverse problem is ill-posed. To solve it, we use the Tikhonov regularization method and minimize the parametric functional with the appropriate stabilizer s cr) ... 

The Tikhonov Regularization Method. We shall dwell briefly on the mathematical aspect of solving the first-kind Fredholm equation by the Tikhonov regularization method, referring basically to the works that deal with the use of this method in the EXAFS spectroscopy [41-44]. The integral equation (92) can be presented in the operator form... 

Experience in using the iterative procedure for solving the inverse problem by the Tikhonov regularization method in EXAFS spectroscopy shows that the obtained solution can be improved by performing a few iterations. 

The Tikhonov regularization method as applied to solving the inverse problem in the SEFS method has the advantage that it allows one to take into account oscillations of two types (oscillations determined by different wave numbers) in the kernel of the integral operator. 

In the current implementation we employ the Tikhonov regularization method (Press et al., 1992. This approach is similar to the constrained density fitting algorithm of Misquitta and Stone (Misquitta and Stone, 2006. Here, the redundant basis set contributions are penalized by minimizing Eseit + resulting... 

As was shown previously [9] Eq. (1) is reduced to the Fredholm integral equation of the first kind, which yields function /(P) after solution via the Tikhonov regularization method. This inverse problem was solved on the basis of an algorithm from [9]. As a result, the function of the distribution over kinetic heterogeneity in /(lnP)-lnM coordinates with each maximum related to the functioning of AC of one type was obtained. 

The previous method may not lead to a unique, physically meaningful spectrum, because the value of G, depends on those of A, and N and contains choices, especially as N increases, it can lead to negative values of G, which are generally thought to be physically unreahstic. To select the true solution from the set of possible solution, Honerkamp and Weese [8, 9] introduced an additional criterion by means of the Tikhonov regularization method. They propose the use of the following condition in place of Eq. (10) ... 

---