We derive a new criterion for a real-valued function u to be in the Sobolev space W 1,2(Rn). This criterion consists of comparing the value of a functional ∫ f (u) with the values of the same functional applied to convolutions of u with a Dirac sequence. The difference of these values converges to zero as the convolutions approach u, and we prove that the rate of convergence to zero is connecte...

We derive strong uniform approximations for the eigenvalues in general Laguerre and Hermite β-ensembles by showing that the maximal discrepancy between the suitably scaled eigenvalues and roots of orthogonal polynomials converges almost surely to zero when the dimension converges to infinity. We also provide estimates of the rate of convergence. In the special case of a normalized real Wishart ...

We derive strong uniform approximations for the eigenvalues in general Laguerre and Hermite β-ensembles by showing that the maximal discrepancy between the suitably scaled eigenvalues and roots of orthogonal polynomials converges almost surely to zero when the dimension converges to infinity. We also provide estimates of the rate of convergence. In the special case of a normalized real Wishart ...

The rate of H-convergence of truncations of stochastic infinite-dimensional systems du = [Au + B(u)]dt + G(u)dW, u(0, ·) = u0 ∈ H with nonrandom, local Lipschitz-continuous operators A,B and G acting on a separable Hilbert space H, where u = u(t, x) : [0, T ] × ID → IRd (ID ⊂ IRd) is studied. For this purpose, some new kind of monotonicity conditions on those operators and an existing H-series ...

We present W-cycle multigrid algorithms for the solution of the linear system of equations arising from a wide class of hp-version discontinuous Galerkin discretizations of elliptic problems. Starting from a classical framework in multigrid analysis, we define a smoothing and an approximation property, which are used to prove the uniform convergence of the W-cycle scheme with respect to the gra...

We show that Sobolev norm convergence of a stationary subdivision scheme is equivalent to standard norm convergence of the stationary subdivision scheme to a limit function in the Sobolev space. Stationary subdivision is an iterative method for the generation of reenable functions which are the main building blocks for the construction of wavelets. For this reason and also because of its use in...

We consider a class of fluid queueing networks with multiple fluid classes and feedback allowed, which are fed by N heavy tailed ON/OFF sources. We study the asymptotic behavior when N → ∞ of these queueing systems in a heavy traffic regime (that is, when they are asymptotically critical). As performance processes we consider the workload W N (the amount of time needed for each server to comple...

In this paper we investigate the zero-relaxation limit of the following multi-D semilinear hyperbolic system in pseudodifferential form: Wt(x, t) + 1 ε A(x, D)W (x, t) = 1 ε B(x, W (x, t)) + 1 ε D(W (x, t)) + E(W (x, t)). We analyse the singular convergence, as ε ↓ 0, in the case which leads to a limit system of parabolic type. The analysis is carried out by using the following steps: (i) We si...

The SOR iteration for solving linear systems of equations depends upon an overrelaxation factor w. We show that for the standard model problem of Poisson’s equation on a rectangle, the optimal w and corresponding convergence rate can be rigorously obtained by Fourier analysis. The trick is to tilt the space-time grid so that the SOR stencil becomes symmetrical. The tilted grid also gives insigh...

Non Linear Discriminant Analysis (NLDA) networks combine a standard Multilayer Perceptron (MLP) transfer function with the minimization of a Fisher analysis criterion. In this work we will define natural-like gradients for NLDA network training. Instead of a more principled approach, that would require the definition of an appropriate Riemannian structure on the NLDA weight space, we will follo...