In the paper we review some known results about the one-sided approximation of polynomials with lower-degree polynomials under L1 norm. Then based on these results, the approximation error is formulated. Some properties are also stated for the general cases. The approximation can be used in the degree reduction of interval polynomials and interval Bézier curves.

This paper derives a novel linear position constraint for cameras seeing a common scene point, which leads to a direct linear method for global camera translation estimation. Unlike previous solutions, this method deals with collinear camera motion and weak image association at the same time. The final linear formulation does not involve the coordinates of scene points, which makes it efficient...

distances Different distances between two given vectors Description These functions are used for calculating different distances between two given vectors. Thus, L1.dist calculates the L1 distance, cosin.dist calculates the cosine distance, euclidian.dist computes the Euclidian distance, and rank.cor.dist computes the rank correlation distance. The vectors have to have same length. When using r...

Inspired by an interesting idea of Cai and Zhang, we formulate and prove the convex k-sparse decomposition of vectors which is invariant with respect to l1 norm. This result fits well in discussing compressed sensing problems under RIP, but we believe it also has independent interest. As an application, a simple derivation of the RIP recovery condition δk + θk,k < 1 is presented.

We present a row-action method based on minimization of the L1 norm for improving the accuracy of fluorescent tomography in reconstruction of fluorescent objects. The method is validated using a CW system and milk-based phantoms.

A singularly perturbed semilinear two point boundary value problem is considered, without any restriction on its turning points. A difference scheme is presented for solving this problem on an arbitrary locally quasiuniform mesh. It is shown that the solution of the scheme is first order accurate, uniformly in the perturbation parameter, in a discrete L1 norm. Numerical results are presented fo...

In the last two decades, many papers have been published, proposing a variety methods of multi-frame resolution enhancement. These methods are usually very sensitive to their assumed model of data and noise, which limits their utility. This paper reviews some of these methods and addresses their shortcomings. We propose a different implementation using L1 norm minimization and robust regulariza...

Generalized H 1 loopshaping is developed for a particular weighted mixed sensitivity minimization task. A free parameter is introduced to trade-oo minimizations of sensitivity and complementary sensitivity in the H 1 performance index. A quadratically convergent algorithm is derived for computing the optimal performance index and a state-space solution is obtained for suboptimal controllers. Th...

It is widely believed that if monotone difference schemes are applied to the linear convection equation with discontinuous initial data, then solutions of the monotone schemes are closer to solutions of their parabolic modified equations than that of the original convection equation. We will confirm the conjecture in this paper. It is well known that solutions of the monotone schemes and their ...