Search results for "REGULARIZATION"

A Note on the Nonlinear Landweber Iteration

2014

We reconsider the Landweber iteration for nonlinear ill-posed problems. It is known that this method becomes a regularization method in the case when the iteration is terminated as soon as the residual drops below a certain multiple of the noise level in the data. So far, all known estimates of this factor are greater than two. Here we derive a smaller factor that may be arbitrarily close to one depending on the type of nonlinearity of the underlying operator equation.

Non-parametric spectrum cartography using adaptive radial basis functions

2017

This paper presents a framework for spectrum cartography based on the use of adaptive Gaussian radial basis functions (RBF) centered around a specific number of centroid locations, which are determined, jointly with the other RBF parameters, by the available measurement values at given sensor locations in a specific geographical area. The spectrum map is constructed non-parametrically as no prior knowledge about the transmitters is assumed. The received signal power at each location (over a given bandwidth and time period) is estimated as a weighted contribution from different RBF, in such a way that the both RBF parameters and the weights are jointly optimized using an alternating minimiza…

Simple regularization scheme for multi-reference density functional theories

2014

Background: Extensions of single-reference (SR) energy-density-functionals (EDFs) to multi-reference (MR) applications involve using the generalized Wick theorem (GWT), which leads to singular energy kernels that cannot be properly integrated to restore symmetries, unless the EDFs are generated by true interactions. Purpose: We propose a new method to regularize the MR EDFs, which is based on using auxiliary quantities obtained by multiplying the kernels with appropriate powers of overlaps. Methods: Regularized matrix elements of two-body interactions are obtained by integrating the auxiliary quantities and then solving simple linear equations. Results: We implement the new regularization m…

On the condition number of the antireflective transform

2010

Abstract Deconvolution problems with a finite observation window require appropriate models of the unknown signal in order to guarantee uniqueness of the solution. For this purpose it has recently been suggested to impose some kind of antireflectivity of the signal. With this constraint, the deconvolution problem can be solved with an appropriate modification of the fast sine transform, provided that the convolution kernel is symmetric. The corresponding transformation is called the antireflective transform. In this work we determine the condition number of the antireflective transform to first order, and use this to show that the so-called reblurring variant of Tikhonov regularization for …

A Douglas–Rachford method for sparse extreme learning machine

2019

Factorization of the soft gluon divergence from the dipole picture deep inelastic scattering cross sections at next-to-leading order

2018

We use a factorization scheme analogous to one proposed for single inclusive forward hadron production to factorize the soft gluon divergence present in the deep inelastic scattering cross sections in the dipole picture at next-to-leading order (NLO). We show numerically that in this carefully constructed scheme it is possible to obtain meaningful results for the DIS cross sections at NLO, and so we are able to quantitatively study the recently derived NLO corrections to the DIS cross sections. We find that the NLO corrections can be significant and sensitive to the details of the factorization scheme used for the resummation of the large logarithms into the BK evolution equation. In the ca…

Analyzing dynamical gluon mass generation

2007

We study the necessary conditions for obtaining infrared finite solutions from the Schwinger-Dyson equation governing the dynamics of the gluon propagator. The equation in question is set up in the Feynman gauge of the background field method, thus capturing a number of desirable features. Most notably, and in contradistinction to the standard formulation, the gluon self-energy is transverse order-by-order in the dressed loop expansion, and separately for gluonic and ghost contributions. Various subtle field-theoretic issues, such as renormalization group invariance and regularization of quadratic divergences, are briefly addressed. The infrared and ultraviolet properties of the obtained so…

ON FRACTIONAL RELAXATION

2003

Generalized fractional relaxation equations based on generalized Riemann-Liouville derivatives are combined with a simple short time regularization and solved exactly. The solution involves generalized Mittag-Leffler functions. The associated frequency dependent susceptibilities are related to symmetrically broadened Cole-Cole susceptibilities occurring as Johari Goldstein β-relaxation in many glass formers. The generalized susceptibilities exhibit a high frequency wing and strong minimum enhancement.

Running couplings from adiabatic regularization

2019

We extend the adiabatic regularization method by introducing an arbitrary mass scale $\mu$ in the construction of the subtraction terms. This allows us to obtain, in a very robust way, the running of the coupling constants by demanding $\mu$-invariance of the effective semiclassical (Maxwell-Einstein) equations. In particular, we get the running of the electric charge of perturbative quantum electrodynamics. Furthermore, the method brings about a renormalization of the cosmological constant and the Newtonian gravitational constant. The running obtained for these dimensionful coupling constants has new relevant (non-logarithmic) contributions, not predicted by dimensional regularization.

A practicableγ 5-scheme in dimensional regularization

1992

We present a new simpleγ5 regularization scheme. We discuss its use in the standard radiative correction calculations including the anomaly contributions. The new scheme features an anticommutingγ5 which leads to great simplifications in practical calculations. We carefully discuss the underlying mathematics of ourγ5-scheme which is formulated in terms of simple projection operations.