Starting from the function values on the roots of Jacobi polynomials, we construct a class of discrete de la Vallée Poussin means, by approximating the Fourier coefficients with a Gauss-Jacobi quadrature rule. Unlike the Lagrange interpolation polynomials, the resulting algebraic polynomials are uniformly convergent in suitable spaces of continuous functions, the order of convergence being comparable with the best polynomial approximation. Moreover, in the four Chebyshev cases the discrete de la Vallée Poussin means share the Lagrange interpolation property, which allows us to reduce the computational cost.

The importance of singular integral transforms, coming from their many applications, justifies some interest in their numerical approximation. Here we propose a stable and convergent algorithm to evaluate such transforms on the real line. Numerical examples confirming the theoretical results are given.

The problem of reconstructing signals and images from degraded ones is considered in this paper. The latter problem is formulated as a linear system whose coefficient matrix models the unknown point spread function and the right hand side represents the observed image. Moreover, the coefficient matrix is very ill-conditioned, requiring an additional regularization term. Different boundary conditions can be proposed. In this paper antireflective boundary conditions are considered. Since both sides of the linear system have uncertainties and the coefficient matrix is highly structured, the Regularized Structured Total Least Squares approach seems to be the more appropriate one to compute an approximation of the true signal/image. With the latter approach the original problem is formulated as an highly nonconvex one, and seldom can the global minimum be computed. It is shown that Regularized Structured Total Least Squares problems for antireflective boundary conditions can be decomposed into single variable subproblems by a discrete sine transform. Such subproblems are then transformed into one-dimensional unimodal realvalued minimization problems which can be solved globally. Some numerical examples show the effectiveness of the proposed approach.

We consider here the problem of tracking the dominant eigenspace of an indefinite matrix by updating recursively a rank k approximation of the given matrix. The tracking uses a window of the given matrix, which increases at every step of the algorithm. Therefore, the rank of the approximation increases also, and hence a rank reduction of the approximation is needed to retrieve an approximation of rank k. In order to perform the window adaptation and the rank reduction in an efficient manner, we make use of a new antitriangular decomposition for indefinite matrices. All steps of the algorithm only make use of orthogonal transformations, which guarantees the stability of the intermediate steps. We also show some numerical experiments to illustrate the performance of the tracking algorithm.

The problem of ship maneuverability has currently reached a significant consideration, both for merchant ships, with the adoption of IMO standards, and naval ships, with the production of various documents by NATO Specialist Teams. In literature, many works regarding maneuverability of single-screw slow/medium speed ships are present, while a lack of information about twin-screw ships (cruise ships, Ro/Ro ferries, megayachts, naval vessels) exists. These ships are usually characterized by different hull forms and more complex stern configuration because of the presence of appendages such as skegs, shaft lines, and brackets, which can strongly affect maneuverability behavior. In this work various prediction methods, namely statistical regressions, system identification, and RANSE, are investigated to evaluate twin-screw naval vessels maneuverability behavior. Results of this analysis clearly evidence importance of stern appendages influence on maneuverability capabilities of this type of ship (including also nonlinear effects resulting from hull/appendage interactions).

We describe a parallel implementation of a compressible Lattice Boltzmann code on a multi-GPU cluster based on Nvidia Fermi processors. We analyze how to optimize the algorithm for GP-GPU architectures, describe the implementation choices that we have adopted and compare our performance results with an implementation optimized for latest generation multi-core CPUs. Our program runs at approximate to 30% of the double-precision peak performance of one GPU and shows almost linear scaling when run on the multi-GPU cluster.