The main goal of our paper is to study the regularization problems which occur in predictive control of systems with severely ill-posed inverse model. We propose a new formulation of predictive control where the future controls are obtained as a solution of certain ill-posed inverse problem. This formulation leads to a possibility of closed loop on-line control of complex systems with ill-posed...

begin{abstract} in this paper, we introduce an iterative method for amenable semigroup of non expansive mappings and infinite family of non expansive mappings in the frame work of hilbert spaces. we prove the strong convergence of the proposed iterative algorithm to the unique solution of a variational inequality, which is the optimality condition for a minimization problem. the results present...

begin{abstract} in this paper, we introduce an iterative method for amenable semigroup of non expansive mappings and infinite family of non expansive mappings in the frame work of hilbert spaces. we prove the strong convergence of the proposed iterative algorithm to the unique solution of a variational inequality, which is the optimality condition for a minimization problem. the results present...

We show that data assimilation using four-dimensional variation (4DVar) can be interpreted as a form of Tikhonov regularisation, a very familiar method for solving ill-posed inverse problems. It is known from image restoration problems that L1-norm penalty regularisation recovers sharp edges in the image more accurately than Tikhonov, or L2-norm, penalty regularisation. We apply this idea to 4D...

The electrocardiographic imaging (ECGI) inverse problem is highly ill-posed and regularization is needed to stabilize the problem and to provide a unique solution. When Tikhonov regularization is used, choosing the regularization parameter is a challenging problem. Mathematically, a suitable value for this parameter needs to fulfill the Discrete Picard Condition (DPC). In this study, we propose...

in this paper, a fundamentally new method, based on the denition, is introduced for numerical computation of eigenvalues, generalized eigenvalues and quadratic eigenvalues of matrices. some examples are provided to show the accuracy and reliability of the proposed method. it is shown that the proposed method gives other sequences than that of existing methods but they still are convergent to t...

image restoration has been an active research area. dierent formulations are eective in high qualityrecovery. partial dierential equations (pdes) have become an important tool in image processingand analysis. one of the earliest models based on pdes is perona-malik model that is a kindof anisotropic diusion (andi) lter. anisotropic diusion lter has become a valuable tool indierent elds...

this paper is concerned with a technique for solving volterra integral equations in the reproducing kernel hilbert space. in contrast with the conventional reproducing kernel method, the gram-schmidt process is omitted here and satisfactory results are obtained.the analytical solution is represented in the form of series.an iterative method is given to obtain the approximate solution.the conver...

It is known, by Rockafellar (SIAM J Control Optim 14:877–898, 1976), that the proximal point algorithm (PPA) converges weakly to a zero of a maximal monotone operator in a Hilbert space, but it fails to converge strongly. Lehdili and Moudafi (Optimization 37:239–252, 1996) introduced the new prox-Tikhonov regularization method for PPA to generate a strongly convergent sequence and established a...

Reconstructing ionospheric electron density (IED) is an ill-posed inverse problem, with classical Tikhonov regularization tending to smooth IED structures. By contrast, total variation (TV) regularization effectively resists noise and preserves discontinuities of the IED. In this paper, we regularize the inverse problem by incorporating both Tikhonov and TV regularization. A specific formulatio...