Operational methods have been used for over a century to solve problems such as ordinary
and partial differential equations. When solving such problems, in many cases it is fairly …

This computationally oriented book describes and explains the mathematical relationships
among matrices, moments, orthogonal polynomials, quadrature rules, and the Lanczos and …

This monograph is a valuable contribution to the highly topical and extremly productive field
of regularisation methods for inverse and ill-posed problems. The author is an internationally …

The retrieval problems arising in atmospheric remote sensing belong to the class of the-
called discrete ill-posed problems. These problems are unstable under data perturbations …

In this paper we propose and analyse a choice of parameters in the multi-parameter
regularization of Tikhonov type. A modified discrepancy principle is presented within the …

The electrical capacitance tomography (ECT) is a promising measurement technique, which
tries to reconstruct the permittivity distribution in a measurement domain by solving an …

We have applied the measurement reduction technique for the ghost imaging (GI) in fiber
optics systems. Ghost images have been reconstructed by numerical simulation of the …

Motivated by the observation that a given signal x admits sparse representations in multiple
dictionaries Ψ d but with varying levels of sparsity across dictionaries, we propose two new …

We consider Tikhonov regularization of large linear discrete ill-posed problems with a
regularization operator of general form and present an iterative scheme based on a …

In this paper, we discuss several (old and new) estimates for the norm of the error in the
solution of systems of linear equations, and we study their properties. Then, these estimates …