We present a weighted BFBT approximation (w-BFBT) to the inverse Schur complement of a Stokes system with highly heterogeneous viscosity. When used as part of a Schur complement-based Stokes preconditioner, we observe robust fast convergence for Stokes problems with smooth but highly varying (up to 10 orders of magnitude) viscosities, optimal algorithmic scalability with respect to mesh refinem...

By the distributed averaging problem is meant the problem of computing the average value ȳ of a set of numbers possessed by the agents in a distributed network using only communication between neighboring agents. Gossiping is a well-known approach to the problem which seeks to iteratively arrive at a solution by allowing each agent to interchange information with at most one neighbor at each it...

We study the problem of minimizing the loss of a linear predictor with a constraint on the `1 norm of the predictor. We describe a forward greedy selection algorithm for this task and analyze its rate of convergence. As a direct corollary of our convergence analysis we obtain a bound on the sparsity of the predictor as a function of the desired optimization accuracy, the bound on the `1 norm, a...

Let the martingale Wn = Zn mn , where Zn is a weighted branching process and m = E ∑ i Ti is the expected sum of the = factors Ti, converge to some limiting random variable W . We give conditions in terms of the factors such that W belongs to the domain of attraction or to the domain of normal attraction of an = α–stable distribution with 1 < α ≤ 2. Further the rate of convergence of Wn to W is...

This document presents some materials not included in the paper. In Section II, we illustrate the direct method for computing l i (w), l − i (w), α + i (w,v) and α − i (w), as well as the approach in Joachims (2006) that is similar to this method. Section III gives a comparison on relative function value, pairwise accuracy and NDCG with respect to the number of (CG) iterations between TRON and ...

We study the convergence of a semidiscrete scheme for the forward-backward parabolic equation ut = (W ′(ux))x with periodic boundary conditions in one space dimension, where W is a standard double-well potential. We characterize the equation satisfied by the limit of the discretized solutions as the grid size goes to zero. Using an approximation argument, we show that it is possible to flow ini...

A systematic study is made of spectral measures in locally convex spaces which are countably additive for the topology of uniform convergence on bounded sets, briefly, the bounded convergence topology. Even though this topology is not compatible for the duality with respect to the pointwise convergence topology it turns out, somewhat surprisingly, that the corresponding L'-spaces for the spectr...

For ψ ∈ W 1,p(Ω;Rm) and g ∈ W−1,p(Ω;Rd), 1 < p < +∞, we consider a sequence of integral functionals F k : W 1,p(Ω;Rm)× Lp(Ω;Rd×n)→ [0,+∞] of the form F k (u, v) =  ∫ Ω fk(x,∇u, v) dx if u− ψ ∈W 1,p 0 (Ω;Rm) and div v = g, +∞ otherwise, where the integrands fk satisfy growth conditions of order p, uniformly in k. We prove a Γ-compactness result for F k with respect to the weak topology of W 1,...