Aggregation–based multigrid with standard piecewise constant like prolongation is investigated. Unknowns are aggregated either by pairs or by quadruplets; in the latter case the grouping may be either linewise or boxwise. A Fourier analysis is developed for a model two– dimensional anisotropic problem. Most of the results are stated for an arbitrary smoother (which fits with the Fourier analysi...

We introduce the sequence spaces [ ˆ w(M)] and [ ˆ w(M)] θ of strong almost convergence and lacunary strong almost convergence respectively defined by the Orlicz function M. We establish certain inclusion relations and show that the above spaces are same for any bounded sequences. 1. Definitions and notations A sequence x ∈ l ∞ , the space of bounded sequences x = (x k), is said to be almost co...

We consider eigenvalues Eλ of the Hamiltonian Hλ= — Δ+ V+ λW, W compactly supported, in the / -> oo limit. For W ̂ 0 we find monotonic convergence of Eλ to the eigenvalues of a limiting operator H^ (associated with an exterior Dirichlet problem), and we estimate the rate of convergence for 1-dimensional systems. In 1-dimensional systems with W^09 or with W changing sign, we do not find convergen...

A weighted median filter is a nonlinear digital filter consisting of a window of length 2N + 1 and a weight vector W -(W-N . . . . . Wo . . . . . WN). A root signal of a median type filter is a signal that is invariant to the filter. However, not all weighted median filters possess the convergence property. In this paper, we shall study the root structures and the convergence behavior of a subc...

We study the regularity of the bilinear maximal operator when applied to Sobolev functions, proving that it maps W (R) × W (R) → W (R) with 1 < p, q < ∞ and r ≥ 1, boundedly and continuously. The same result holds on R when r > 1. We also investigate the almost everywhere and weak convergence under the action of the classical Hardy-Littlewood maximal operator, both in its global and local versi...

•Common choice is Metropolis-Hastings: W M H i j = { 1/(2dmax) if {i , j } ∈ E 1−di /(2dmax) if i = j 0 otherwise •Rate of convergence is controlled by ρ(W −11T /n). • min{ρ(W −11T /n) : W symmetrical} is a convex problem (SDP). •Optimal matrix yields slow rate O(D2), achieved by W M H . •Lower-bound: Ω(D), where D is graph diameter. •To get fast rates, two approaches have been developed indepe...

There has been an enormous amount of work on error estimates for approximate solutions to scalar conservation laws. The methods of analysis include matching the traveling wave solutions, [8, 24]; matching the Green function of the linearized problem [21]; weak W convergence theory [32]; the Kruzkov-functional method [19]; and the energy-like method [34]. The results on error estimates include: ...

Our starting point is the Mosco-convergence result due to Hess ((He'89]) for integrable multivalued supermartingales whose values may be unbounded, but are majorized by a w-ball-compact-valued function. It is shown that the convergence takes place also in the slice topology. In the case when both the underlying space X and its dual X have the Radon-Nikodym property a weaker compactness assumpti...

An integral representation for the relaxation in BV(Q; W) of the functional with respect to BV weak • convergence is obtained. The bulk term in the integral representation reduces to QW, the quasiconvexification of W, and it is shown exactly how optimal approximating sequences behave along 5(u), for scalar valued u.

Consider a generalized linear model with response Y and scalar predictor X. Instead of observing X, a surrogate W = X + Z is observed where Z represents measurement error and is independent of X and Y. The efficient score test for the absence of association depends on m(w) = E(XIW = w) which is generally unknown (Tosteson and Tsiatis, 1988). Assuming that the distribution of Z is known, asympto...