The article considers a new iterative algorithm for solving total least squares problems. A version of the implicit method simple iterations based on singular value decomposition is proposed biased normal system algebraic equations. use makes it possible to replace an ill-conditioned problem with sequence problems smaller condition number. This significantly increase computational stability and...

In this work, we analyze the behavior of the active-set method for the nonnegative regularization of discrete ill-posed problems. In many applications, the solution of a linear ill-posed problem is known to be nonnegative. Standard Tikhonov regularization often provides an approximated solution with negative entries. We apply the activeset method to find a nonnegative approximate solution of th...

This paper studies iterative learning control (ILC) for under-determined and over-determined systems, i.e., systems for which the control action to produce the desired output is not unique, or for which exact tracking of the desired trajectory is not feasible. For both cases we recommend the use of the pseudoinverse or its approximation as a learning operator. The Tikhonov regularization techni...

We consider solution of linear ill-posed problem Au = f by Tikhonov method and by Lavrentiev method. For increasing the qualification and accuracy of these methods we use extrapolation, taking for the approximate solution linear combination of n ≥ 2 approximations of Tikhonov or Lavrentiev methods with different parameters and with proper coefficients. If the solution u∗ belongs to R((A A)) and...

We consider the problem of finding regularized solutions to ill-posed Volterra integral equations. The method we consider is a sequential form of Tikhonov regularization that is particularly suited to problems of Volterra type. We prove that when this sequential regularization method is coupled with several standard discretizations of the integral equation (collocation, rectangular and midpoint...

in this paper the 3d inversion of gravity data using two different regularization methods, namely tikhonov regularization and truncated singular value decomposition (tsvd), is considered. the earth under the survey area is modeled using a large number of rectangular prisms, in which the size of the prisms are kept fixed during the inversion and the values of densities of the prisms are the mode...

We present a method for the solution of 3-D controlled source magnetotelluric (CSAMT) inverse problems. The inverse problem is formulated as the minimization of a Tikhonov parametric functional with a focusing stabilizer. Observed CSAMT apparent resis­ tivities are converted to log-anomalous apparent resistivities, which are linearly connected to anomalous currents via the integral equation. We...

Early diagnosis of stroke type by imaging is one the most important tasks for patients. In this article, we propose a new approach to reconstruct brain image with high accuracy and quality. approach, first use Born iterative method image. Then comparing set MRI-based images, using structural similarity index measure criterion, choose best as reference Finally, distorted or along generalized Tik...