The carré du champ method is a powerful technique for proving interpolation inequalities with explicit constants in presence of non-trivial metric on manifold. applies to some classical Gagliardo-Nirenberg-Sobolev the sphere, optimal constants. Very nonlinear regimes close critical Sobolev exponent can be covered using parabolic flows porous medium or fast diffusion type. Considering power law ...

Topographic maps are commonly constructed from electrical scalp recordings (such as EEGs and ERPs) using several different interpolation methods. It is important to determine the accuracy of such maps. Previous assessments of interpolation methods have been based on global error measures and the visual appearance of the topographic maps. However, the relationship of interpolation error to local...

We address the problem of data independent robust array interpolation over large angular sectors. Previous interpolation methods apply the root-MUSIC principle to interpolation data of a predefined virtual ULA manifold. These methods either suffer from severely biased direction-ofarrival estimates due to interpolation errors or rely on data dependent interpolation matrix design. In this paper a...

so far several methods have been developed for mapping and interpolation of isohyets.one of the recently accepted methods is geographically weighting regression which is suitable for evaluation of spatial heterogeneity of dependent variable by using local regressions. in order to evaluate annually precipitation spatial variation, this study was conducted in gilan province which precipitation is...

We consider the problem of image interpolation from an adaptive optimal recovery point of view. Many different standard interpolation approaches may be viewed through the prism of optimal recovery. In this paper we review some standard image interpolation methods and how they relate to optimal recovery as well as introduce a broader, more general and systematic approach to image interpolation u...