By coupling the wavelet transform with a particular nonlinear shrinking function, the Red-telescopic optimal wavelet estimation of the risk (TOWER) method is introduced for removing noise from signals. It is shown that the method yields convergence of the L2 risk to the actual solution with optimal rate. Moreover, the method is proved to be asymptotically efficient when the regularization parameter is selected by the generalized cross validation criterion (GCV) or the Mallows criterion. Numerical experiments based on synthetic data are provided to compare the performance of the Red-TOWER method with hard-thresholding, soft-thresholding, and neigh–coeff thresholding. Furthermore, the numerical tests are also performed when the TOWER method is applied to hard-thresholding, soft-thresholding, and neigh–coeff thresholding, for which the full convergence results are still open.

We deal with the numerical evaluation of the Hilbert transform on the real line by a Gauss type quadrature rule. The convergence and the stability of the method are investigated. The goodness of the numerical results for practical applications is examined.

A semi-implicit semi-Lagragian mixed finite-difference finite-volume model for the shallow water equations on a rotating sphere is considered The main features of the model are the finite-volume approach for the continuity equation and the vectorial treatment of the momentum equation. Pressure and Coriolis terms in the momentum equation and velocity in the continuity equation are treated semi-implicitly. Discretization of this model led to the introducion, in a previous paper, of a splitting technique which highly reduces the computational effort for the numerical solution. In this paper we solve the full set of equations, without splitting, introducing an ad hoc algorithm A von Neumann stability analysis of this scheme is performed to establish the unconditional stability of the new proposed method Finally, we compare the efficiency of the two approaches by numerical experiments on a standard test problem Results show that due to the devised algorithm, the solution of the full system of equations is much more accurate while slightly increasing the computational cost. A semi-implicit semi-Lagrangian mixed finite-difference finite-volume model for the shallow water equations on a rotating sphere is considered. The main features of the model are the finite-volume approach for the continuity equation and the vectorial treatment of the momentum equation. Pressure and Coriolis terms in the momentum equation and velocity in the continuity equation are treated semi-implicitly. Discretization of this model led us to introduce, in a previous paper, a splitting technique which highly reduces the computational effort for the numerical solution. In this paper we solve the full set of equations, without splitting, introducing an 'ad hoc' algorithm. A von Neumann stability analysis of this scheme is performed to establish the unconditional stability of the new proposed method. Finally, we compare the efficiency of the two approaches by numerical experiments on a standard test problem. Our results show that, due to the devised algorithm, the solution of the full system of equations is much more accurate while slightly increases the computational cost.

Conditions are proven which assure the summability of the first difference of the fundamental matrix of nonconvolution Volterra discrete equations. These conditions are applied to the \st analysis of some linear methods for solving Volterra integral equations of nonconvolution type.

We study general over-relaxation Markov Chain Monte Carlo samplers for multivariate Gaussian densities. We provide conditions for convergence based on the spectral radius of the transition matrix and on detailed balance. We illustrate these algorithms using an image analysis example.

An algorithm for the approximate evaluation of the Hilbert transform has been proposed. The convergence of the procedure is proved. The stability of the algorthim is considered and some numerical examples are given.

We propose a semilinear relaxation approximation to the unique entropy solutions of an initial boundary value problem for a scalar conservation law. Without any restriction on the initial--boundary data or on the flux function, we prove uniform a priori estimates and convergence of that approximation as the relaxation parameter tends to zero.

It iswell-knownthat multivariate curve estimation suffers from the “curse of dimensionality.”However, reasonable estimators are possible, even in several dimensions, under appropriate restrictions on the complexity of the curve. In the present paper we explore how much appropriate wavelet estimators can exploit a typical restriction on the curve such as additivity. We first propose an adaptive and simultaneous estimation procedure for all additive components in additive regression models and discuss rate of convergence results and data-dependent truncation rules for wavelet series estimators. To speed up computation we then introduce a wavelet version of functional ANOVA algorithm for additive regression models and propose a regularization algorithm which guarantees an adaptive solution to the multivariate estimation problem. Some simulations indicate that wavelets methods complement nicely the existing methodology for nonparametric multivariate curve estimation.

In this paper we study several different methods both deterministic and stochastic to solve the Nuclear Magnetic Resonance (NMR) relaxometry problem. This problem is strongly related to finding a non-negative function given a finite number of values of its Laplace transform embedded in noise. Some of the methods considered here are new. We also propose a procedure which exploits and combines the main features of these methods. To show the performances of this procedure, some results of applying it to synthetic data are finally reported.

By improving a one-dimensional model proposed by De Fabritiis, Mancini, Mansutti and Succi in 1998, we develop a simple reaction model for liquid-solid phase transitions in the context of the lattice Boltzmann method with enhanced collisions.Calculations for a two-dimensional test problem of gallium melting and for a two-dimensional anisotropic growth of dendrites are presented and commented on.