We analyze the asymptotic convergence of all infinite products of matrices taken in a given finite set by looking only at finite or periodic products. It is known that when the matrices of the set have a common nonincreasing polyhedral norm, all infinite products converge to zero if and only if all infinite periodic products with periods smaller than a certain value converge to zero. Moreover, ...

A mathematical analysis is presented for a class of interior penalty (IP) discontinuous Galerkin approximations of elliptic boundary value problems. In the framework of the present theory one can derive some overpenalized IP bilinear forms avoiding the notion of fluxes and artificial penalty terms. The main idea is to start from bilinear forms for the local average of discontinuous approximatio...

In this paper we analyze, mainly in a finitary setting, the consistency properties of fuzzy possibilities, interpreting them as instances of upper previsions and applying the basic notions of avoiding sure loss and coherence from the theory of imprecise probabilities. It ensues that fuzzy possibilities always avoid sure loss, but satisfy the stronger coherence condition only in a special case. ...

We consider estimating an unknown signal, which is both blocky and sparse, corrupted by additive noise. We study three interrelated least squares procedures and their asymptotic properties. The first procedure is the fused lasso, put forward by Friedman et al. (2007), which we modify into a different estimator, called the fused adaptive lasso, with better properties. The other two estimators we...

Robust dynamic programming (robust DP) mitigates the effects of ambiguity in transition probabilities on the solutions of Markov decision problems. We consider the computation of robust DP solutions for discrete-stage, infinite-horizon, discounted problems with finite state and action spaces. We present robust modified policy iteration (RMPI) and demonstrate its convergence. RMPI encompasses bo...

This paper considers the use of the anisotropic total variation seminorm to recover a two dimensional vector x ∈ CN×N from its partial Fourier coefficients, sampled along Cartesian lines. We prove that if (xk,j − xk−1,j)k,j has at most s1 nonzero coefficients in each column and (xk,j − xk,j−1)k,j has at most s2 nonzero coefficients in each row, then, up to multiplication by log factors, one can...

This article deals with a first-order least-squares approach to the solution of an optimal control problem governed by Stokes equations. As with our earlier work on a velocity control by the Stokes flow in [S. Ryu, H.-C. Lee and S. D. Kim, SIAM J. Numer. Anal., 47 (2009), pp. 1524-1545], we recast the objective functional as a H1 seminorm in the velocity control term. By introducing a velocity-...

We study Γ-convergence of graph-based Ginzburg–Landau functionals, both the limit for zero diffusive interface parameter ε → 0 and the limit for infinite nodes in the graph m→∞. For general graphs we prove that in the limit ε → 0 the graph cut objective function is recovered. We show that the continuum limit of this objective function on 4-regular graphs is related to the total variation semino...

For a closed cocompact subgroup Γ of a locally compact group G, given a compact abelian subgroup K of G and a homomorphism ρ : K̂ → G satisfying certain conditions, Landstad and Raeburn constructed equivariant noncommutative deformations C∗(Ĝ/Γ, ρ) of the homogeneous space G/Γ, generalizing Rieffel’s construction of quantum Heisenberg manifolds. We show that when G is a Lie group and G/Γ is conn...

such that (i) |0| = 0, (ii) |x| ≥ 0, for all x ∈ X , (iii) |− x| = |x|, for all x ∈ X , (iv) |x+ y| ≤ |x|+ |y|, for all x, y ∈ X , (v) if tk ∈ F, |tk − t| → 0, and xk, x ∈ X , |xk − x| → 0, then |tkxk − tx| → 0. If | · | satisfies only properties (i) to (iv), then we call | · | a near quasinorm. If the quasinorm satisfies |x| = 0 if and only if x = 0, then it is said to be total. A quasinormed ...