Maria Rosaria Russo

Embedded techniques for choosing the parameter in tikhonov regularization

SUMMARY This paper introduces a new strategy for setting the regularization parameter when solving large-scale discrete ill-posed linear problems by means of the Arnoldi–Tikhonov method. This new rule is essentially based on the discrepancy principle, although no initial knowledge of the norm of the error that affects the right-hand side is assumed; an increasingly more accurate approximation of this quantity is recovered during the Arnoldi algorithm. Some theoretical estimates are derived in order to motivate our approach. Many numerical experiments performed on classical test problems as well as image deblurring problems are presented. Copyright

Adaptive Arnoldi-Tikhonov regularization for image restoration

In the framework of the numerical solution of linear systems arising from image restoration, in this paper we present an adaptive approach based on the reordering of the image approximations obtained with the Arnoldi-Tikhonov method. The reordering results in a modified regularization operator, so that the corresponding regularization can be interpreted as problem dependent. Numerical experiments are presented.

An approach to the Gummel map by vector extrapolation methods

The numerical approximation of nonlinear partial differential equations requires the computation of large nonlinear systems, that are typically solved by iterative schemes. At each step of the iterative process, a large and sparse linear system has to be solved, and the amount of time elapsed per step grows with the dimensions of the problem. As a consequence, the convergence rate may become very slow, requiring massive cpu-time to compute the solution. In all such cases, it is important to improve the rate of convergence of the iterative scheme. This can be achieved, for instance, by vector extrapolation methods. In this work, we apply some vector extrapolation methods to the electronic device simulation to improve the rate of convergence of the family of Gummel decoupling algorithms. Furthermore, a different approach to the topological ε-algorithm is proposed and preliminary results are presented.

An accelerated algorithm for Navier-Stokes equations

Abstract In this paper, the numerical solution of the Navier–Stokes equations by the Characteristic-Based-Split (CBS) scheme is accelerated with the Minimum Polynomial Extrapolation (MPE) method to obtain the steady state solution for evolution incompressible and compressible problems. The CBS is essentially a fractional time-stepping algorithm based on an original finite difference velocity-projection scheme where the convective terms are treated using the idea of the Characteristic-Galerkin method. In this work, the semi-implicit version of the CBS with global time-stepping is used for incompressible problems whereas the fully-explicit version is used for compressible flows. At the other end, the MPE is a vector extrapolation method that transforms the original sequence into another sequence converging to the same limit faster then the original one without the explicit knowledge of the sequence generator. The developed algorithm, tested on two-dimensional benchmark problems, demonstrates the new computational features arising from the introduction of the extrapolation procedure to the CBS scheme. In particular, the results show a remarkable reduction of the computational cost of the simulation.