Optimal Lp-Metric for Minimizing Powered Deviations in Regression

Optimal Lp-Metric for Minimizing Powered Deviations in Regression

Optimal anisotropic meshes for minimizing interpolation errors in Lp-norm

In this paper, we present a new optimal interpolation error estimate in Lp norm (1 ≤ p ≤ ∞) for finite element simplicial meshes in any spatial dimension. A sufficient condition for a mesh to be nearly optimal is that it is quasi-uniform under a new metric defined by a modified Hessian matrix of the function to be interpolated. We also give new functionals for the global moving mesh method and ...

Approximately Optimal Mechanisms for Strategyproof Facility Location: Minimizing Lp Norm of Costs

We consider the problem of locating a single facility on the real line. This facility serves a set of agents, each of whom is located on the line, and incurs a cost equal to his distance from the facility. An agent’s location is private information that is known only to him. Agents report their location to a central planner who decides where to locate the facility. The planner’s objective is to...

Metric Minimizing Surfaces

Consider a two-dimensional surface in an Alexandrov space of curvature bounded above by k. Assume that this surface does not admit contracting deformations (a particular case of such surfaces is formed by area minimizing surfaces). Then this surface inherits the upper curvature bound, that is, this surface has also curvature bounded above by k, with respect to the intrinsic metric induced from ...

Perfect codes in the lp metric

We investigate perfect codes in Zn in the `p metric. Upper bounds for the packing radius r of a linear perfect code in terms of the metric parameter p and the dimension n are derived. For p = 2 and n = 2, 3, we determine all radii for which there exist linear perfect codes. The non-existence results for codes in Zn presented here imply non-existence results for codes over finite alphabets Zq, w...