The kernel null-space technique is known to be an effective one-class classification (OCC) technique. Nevertheless, the applicability of this method limited due its susceptibility possible training data corruption and inability rank observations according their conformity with model. This article addresses these shortcomings by regularizing solution Fisher methodology in context regression-base...

The generalized singular value decomposition (GSVD) often is used to solve Tikhonov regularization problems with a regularization matrix without exploitable structure. This paper describes how the standard methods for the computation of the GSVD of a matrix pair can be simplified in the context of Tikhonov regularization. Also, other regularization methods, including truncated GSVD, are conside...

in this work, a new iterative method is proposed for obtaining the approximate solution of a class of hammerstein type integral equations system. the main structure of this method is based on the richardson iterative method for solving an algebraic linear system of equations. some conditions for existence and unique solution of this type equations are imposed. convergence analysis and error bou...

In this paper, we propose an algorithm for numerical solving an inverse non-linear diusion problem. In additional, the least-squares method is adopted tond the solution. To regularize the resultant ill-conditioned linear system ofequations, we apply the Tikhonov regularization method to obtain the stablenumerical approximation to the solution. Some numerical experiments con-rm the utility of th...

In this article parameter estimation problems for a nonlinear elliptic problem are considered. Using Tikhonov regularization techniques the identification problems are formulated in terms of optimal control problems which are solved numerically by an augmented Lagrangian method combined with a globalized sequential quadratic programming algorithm. For the discretization of the partial different...

In many industrial applications, such as in the steel industry, it is important to monitor surface temperature, and also heating or cooling rates, during an process. However, often may be inaccessible for direct measurements. Instead we are restricted using interior measurements estimate by solving inverse heat conduction problem. The problem well-known has been studied authors. this paper a no...

This paper is concerned with the inverse problem of determining time and space dependent source term diffusion equations constant-order time-fractional derivative in $(0,2)$. We examine two different cases. In first one, product spatial temporal terms, we prove that both them can be retrieved by knowledge one arbitrary internal measurement solution for all times. second case, assume varies fixe...

In this paper, we analyze a sparse nonlinear inverse scattering problem arising in microwave imaging and numerically solved it for retrieving dielectric contrast from measured fields. In sparsity reconstruction, contrast profiles are a priori assumed to be sparse with respect to a certain base. We proposed an approach which is motivated by a Tikhonov functional incorporating a sparsity promotin...

It is a common belief that Tikhonov scheme with ‖ · ‖L2 -penalty fails to reconstruct a sparse structure with respect to a given system {φi}. However, in this paper we present a procedure for sparsity reconstruction, which is totally based on the standard Tikhonov method. This procedure consists of two steps. At first Tikhonov scheme is used as a sieve to find the coefficients near φi, which ar...