All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 8 Next

Displaying 141 – 160 of 186

Showing per page

s∗-compressibility of the discrete Hartree-Fock equation

Heinz-Jürgen Flad, Reinhold Schneider (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

The Hartree-Fock equation is widely accepted as the basic model of electronic structure calculation which serves as a canonical starting point for more sophisticated many-particle models. We have studied the s∗-compressibility for Galerkin discretizations of the Hartree-Fock equation in wavelet bases. Our focus is on the compression of Galerkin matrices from nuclear Coulomb potentials and nonlinear terms in the Fock operator which hitherto has not been discussed in the literature. It can be shown...

Signal reconstruction from given phase of the Fourier transform using Fejér monotone methods

Dieter Schott (2000)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

The aim is to reconstruct a signal function x ∈ L₂ if the phase of the Fourier transform [x̂] and some additional a-priori information of convex type are known. The problem can be described as a convex feasibility problem. We solve this problem by different Fejér monotone iterative methods comparing the results and discussing the choice of relaxation parameters. Since the a-priori information is partly related to the spectral space the Fourier transform and its inverse have to be applied in each...

Solving singular convolution equations using the inverse fast Fourier transform

Eduard Krajník, Vincente Montesinos, Peter Zizler, Václav Zizler (2012)

Applications of Mathematics

The inverse Fast Fourier Transform is a common procedure to solve a convolution equation provided the transfer function has no zeros on the unit circle. In our paper we generalize this method to the case of a singular convolution equation and prove that if the transfer function is a trigonometric polynomial with simple zeros on the unit circle, then this method can be extended.

Sparse data structure design for wavelet-based methods

Guillaume Latu (2011)

ESAIM: Proceedings

This course gives an introduction to the design of efficient datatypes for adaptive wavelet-based applications. It presents some code fragments and benchmark technics useful to learn about the design of sparse data structures and adaptive algorithms. Material and practical examples are given, and they provide good introduction for anyone involved in the development of adaptive applications. An answer will be given to the question: how to implement and efficiently use the discrete wavelet transform...

Sparse finite element methods for operator equations with stochastic data

Tobias von Petersdorff, Christoph Schwab (2006)

Applications of Mathematics

Let A V → V ' be a strongly elliptic operator on a d -dimensional manifold D (polyhedra or boundaries of polyhedra are also allowed). An operator equation A u = f with stochastic data f is considered. The goal of the computation is the mean field and higher moments ℳ 1 u ∈ V , ℳ 2 u ∈ V ⊗ V , ... , ℳ k u ∈ V ⊗ ⋯ ⊗ V of the solution. We discretize the mean field problem using a FEM with hierarchical basis and N degrees of freedom. We present a Monte-Carlo algorithm and a deterministic algorithm for the approximation of the moment ℳ k u for k ≥ 1 . The key tool...

Sparse grids for the Schrödinger equation

Michael Griebel, Jan Hamaekers (2007)

ESAIM: Mathematical Modelling and Numerical Analysis

We present a sparse grid/hyperbolic cross discretization for many-particle problems. It involves the tensor product of a one-particle multilevel basis. Subsequent truncation of the associated series expansion then results in a sparse grid discretization. Here, depending on the norms involved, different variants of sparse grid techniques for many-particle spaces can be derived that, in the best case, result in complexities and error estimates which are independent of the number of particles. Furthermore...

Spectral reconstruction of piecewise smooth functions from their discrete data

Anne Gelb, Eitan Tadmor (2002)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

This paper addresses the recovery of piecewise smooth functions from their discrete data. Reconstruction methods using both pseudo-spectral coefficients and physical space interpolants have been discussed extensively in the literature, and it is clear that an a priori knowledge of the jump discontinuity location is essential for any reconstruction technique to yield spectrally accurate results with high resolution near the discontinuities. Hence detection of the jump discontinuities is critical...

Spectral Reconstruction of Piecewise Smooth Functions from Their Discrete Data

Anne Gelb, Eitan Tadmor (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

This paper addresses the recovery of piecewise smooth functions from their discrete data. Reconstruction methods using both pseudo-spectral coefficients and physical space interpolants have been discussed extensively in the literature, and it is clear that an a priori knowledge of the jump discontinuity location is essential for any reconstruction technique to yield spectrally accurate results with high resolution near the discontinuities. Hence detection of the jump discontinuities is critical...

Ternary wavelets and their applications to signal compression

Ghulam Mustafa, Falai Chen, Zhangjin Huang (2004)

International Journal of Applied Mathematics and Computer Science

We introduce ternary wavelets, based on an interpolating 4-point C^2 ternary stationary subdivision scheme, for compressing fractal-like signals. These wavelets are tightly squeezed and therefore they are more suitable for compressing fractal-like signals. The error in compressing fractal-like signals by ternary wavelets is at most half of that given by four-point wavelets (Wei and Chen, 2002). However, for compressing regular signals we further classify ternary wavelets into 'odd ternary' and 'even...

Currently displaying 141 – 160 of 186