A multilevel method on adaptive meshes with hanging nodes is derived. Smoothing is restricted to the interior of the subdomains refined to the current level, thus has optimal computational complexity. Its convergence rates are the same as for the the non-adaptive version. We discuss the implementation in a general finite element code at the example of the deal.II library.

The paper presents a unified approach to local likelihood estimation for a broad class of nonparametric models, including e.g. the regression, density, Poisson and binary response model. The method extends the adaptive weights smoothing (AWS) procedure introduced in Polzehl and Spokoiny (2000) in context of image denois-ing. Performance of the proposed procedure is illustrated by a number of nu...

In several applications where binary contours are used to represent and classify patterns, smoothing must be performed to attenuate noise and quantization error. This is often implemented with local weighted averaging of contour point coordinates, because of the simplicity, low-cost and eeectiveness of such methods. Invoking thèoptimality' of the Gaussian lter, many authors will use Gaussian-de...

There are several Global Climate Models (GCMs) reported by various countries to the Intergovernmental Panel on Climate Change (IPCC). Due to the varied nature of the GCM assumptions, the future projections of the GCMs show high variability which makes it difficult to come up with confident projections into the future. Climate scientists combine these multiple GCMs to minimize the variability an...

Penalized likelihood methods provide a range of practical modelling tools, including spline smoothing, generalized additive models and variants of ridge regression. Selecting the correct weights for penalties is a critical part of using these methods and in the single penalty case the analyst has several well founded techniques to choose from. However, many modelling problems suggest a formulat...

We consider ®rst the spline smoothing nonparametric estimation with variable smoothing parameter and arbitrary design density function and show that the corresponding equivalent kernel can be approximated by the Green function of a certain linear differential operator. Furthermore, we propose to use the standard (in applied mathematics and engineering) method for asymptotic solution of linear d...

This article considers the application of the unscented transformation to approximate fixed-interval optimal smoothing of continuous-time non-linear stochastic systems. The proposed methodology can be applied to systems, where the dynamics can be modeled with non-linear stochastic differential equations and the noise corrupted measurements are obtained continuously or at discrete times. The smo...

It is widely believed that in order to solve large scale global optimization problems an appropriate mixture of local approximation and global exploration is necessary. Local approximation, if first order information on the objective function is available, is efficiently performed by means of local optimization methods. Unfortunately, global exploration, in absence of some kind of global inform...