A method for lossy compression of genus-0 surfaces is presented. Geometry, texture and other surface attributes are incorporated in a unified manner. The input surfaces are represented by surfels (surface elements), i.e., by a set of disks with attributes. Each surfel, with its attribute vector, is optimally mapped onto a sphere in the sense of geodesic distance preservation. The resulting sphe...

In a recent paper, we analyzed the properties of a new kind of spherical wavelets (called needlets) for statistical inference procedures on spherical random fields; the investigation was mainly motivated by applications to cosmological data. In the present work, we exploit the asymptotic uncorrelation of random needlet coefficients at fixed angular distances to construct subsampling statistics ...

[1] We determine a regional spatiotemporal gravity field over northern South America including the Amazon region using GRACE inter-satellite range-rate measurements by application of a wavelet-based multiresolution technique. A major advantage of this method is that we are able to represent the Amazon hydrological signals in form of time series of detail signals with level-dependent temporal re...

A general framework is introduced to analyze the approximation properties of mapped Legendre polynomials and of interpolations based on mapped Legendre–Gauss–Lobatto points. Optimal error estimates featuring explicit expressions on the mapping parameters for several popular mappings are derived. These results not only play an important role in numerical analysis of mapped Legendre spectral and ...

The principle result of this paper is the following operational Tau method based upon Müntz-Legendre polynomials. This methodology provides a computational technique for numerical solution of fractional differential equations by using a sequence of matrix operations. The main property of Müntz polynomials is that fractional derivatives of these polynomials can be expressed in terms of the same ...

We consider a fourth-order eigenvalue problem on a semi-infinite strip which arises in the study of viscoelastic shear flow. The eigenvalues and eigenfunctions are computed by a spectral method involving Laguerre functions and Legendre polynomials.

Current spectral simulations of Einstein’s equations require writing the equations in first-order form, potentially introducing instabilities and inefficiencies. We present a new penalty method for pseudospectral evolutions of second order in space wave equations. The penalties are constructed as functions of Legendre polynomials and are added to the equations of motion everywhere, not only on ...