• Sparse iterative linear solvers are the most important building block in (implicit) schemes for PDE problems • In FD, FV and FE discretisations • Lots of research on GPUs so far for Krylov subspace methods, ADI approaches and multigrid • But: Limited to simple preconditioners and smoothing operators •Numerically strong smoothers exhibit inherently sequential data dependencies (impossible to p...

We propose to combine smoothing, simulations and sieve approximations solve for either the integrated or expected value function in a general class of dynamic discrete choice (DDC) models. use importance sampling approximate Bellman operators defining two functions. The random operators, therefore also corresponding solutions, are generally non-smooth which is undesirable. To circumvent this is...

In this paper we present an effective unsupervised colour image segmentation algorithm which uses multiscale edge information and spatial colour content. The multiscale edge information is extracted using the dual-tree complex wavelet transform. Binary morphological operators are applied to the edge information to detect seed regions which are large enough to exclude boundaryonly regions. The s...

This study considers four means of defining differential operators for extracting local aspects of shape in ill-specified environments: fuzzy differentiation as kernel smoothing; differentiation in the sense of weak or generalized derivatives; differentiation for fuzzy functions between normed spaces; and fuzzy differentiation for mappings between fuzzy manifolds. More consideration is given to...

Based on the class of complex gradient-Laplace operators, we show the design of a non-separable two-dimensional wavelet basis from a single and analytically defined generator wavelet function. The wavelet decomposition is implemented by an efficient FFT-based filterbank. By allowing for slight redundancy, we obtain the Marr wavelet pyramid decomposition that features improved translation-invari...

Old documents frequently appear with digitalization errors, uneven background, bleed-through effect etc... Motivated by the challenge to improve printed and handwritten text, we developed a new approach based on morphological color operators using HSI color space. Our approach is composed of a morphological background estimation for foreground/background separation and text segmentation, a back...

It is neither feasible nor desirable to consider in detail all of the small-scale fluctuations that occur in the atmosphere. For this reason, we introduce averaging or smoothing operators, and attempt to describe only the average state of the atmosphere, following the approach of “Reynolds Averaging.” This leads, however, to additional terms in the governing equations for the averaged quantitie...

In the description of the long-time behavior of solutions to nonautonomous differential equations the notion of a pullback attractor plays a similar role as the global attractor in autonomous dynamical systems. We present the theorem on the existence of a pullback attractor if the evolution process is a family of closed operators. The abstract result is formulated in the context of the smoothin...

Wavelets are a powerful tool for planar image processing. The resulting algorithms are straightforward, fast, and efficient. With the recently developed spherical wavelets this framework can be transposed to spherical textures. We describe a class of processing operators which are diagonal in the wavelet basis and which can be used for smoothing and enhancement. Since the wavelets (filters) are...

8 In this paper, we study the error of a second order finite difference scheme for the one-dimensional 9 convection-diffusion equation. We consider non-smooth initial conditions commonly encountered in 10 financial pricing applications. For these initial conditions, we establish the explicit expression of the 11 quantization error, which is loosely defined as the error of the numerical solution...