In this work, the bilinear nite element method on a Shishkin mesh for convection-diiusion problems is analyzed in the two-dimensional setting. A su-perconvergent rate O(N ?2 ln 2 N + N ?3=2) in a discrete-weighted energy norm is established under certain regularity assumption. This convergent rate is uniformly valid with respect to the singular perturbation parameter. Numerical tests indicate t...

In this work, the bilinear finite element method on a Shishkin mesh for convection-diffusion problems is analyzed in the two-dimensional setting. A superconvergence rate O(N−2 ln N + N−1.5 lnN) in a discrete -weighted energy norm is established under certain regularity assumptions. This convergence rate is uniformly valid with respect to the singular perturbation parameter . Numerical tests ind...

This paper presents a simple but robust visual tracking algorithm based on representing the appearances of objects using affine warps of learned linear subspaces of the image space. The tracker adaptively updates this subspace while tracking by finding a linear subspace that best approximates the observations made in the previous frames. Instead of the traditional L-reconstruction error norm wh...

The smooth approximation and weighted energy estimates for delta 6-convex functions are derived in this research. Moreover, we conclude that if 6-convex functions are closed in uniform norm, then their third derivatives are closed in weighted [Formula: see text]-norm.

Let X be a WCG Banach space admitting a Ck-Fréchet smooth norm. Then X admits an equivalent norm which is simultaneously C1-Fréchet smooth, LUR, and a uniform limit of Ck-Fréchet smooth norms. If X = C([0, α]), where α is an ordinal, then the same conclusion holds true with k =∞.

We study a class of symmetric discontinuous Galerkin methods on graded meshes. Optimal order error estimates are derived in both the energy norm and the L2 norm, and we establish the uniform convergence of V -cycle, F -cycle and W -cycle multigrid algorithms for the resulting discrete problems. Numerical results that confirm the theoretical results are also presented.

This paper addresses the problem of estimating a convex regression function under both the sup-norm risk and the pointwise risk using B-splines. The presence of the convex constraint complicates various issues in asymptotic analysis, particularly uniform convergence analysis. To overcome this difficulty, we establish the uniform Lipschitz property of optimal spline coefficients in the `∞-norm b...

in this paper,~some results on finite dimensional generating spaces of quasi-norm family are established.~the idea of equivalent quasi-norm families is introduced.~riesz lemma is established in this space.~finally,~we re-define b-s fuzzy norm and prove that it induces a generating space of quasi-norm family.

Our main interest in this paper is approximation of a continuous function, on a finite interval, which changes convexity finitely many times by algebraic polynomials which are coconvex with it. This topic has received much attention in recent years, and the purpose of this paper is to give final answers to open questions concerning the validity of Jackson type estimates involving the weighted D...