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An alternative to Ewald sums
(1994)SAM Research ReportIn this paper identities are derived which allow to compute the Coulomb energy associated with emN/em charges in a central cell and all their periodic images. These identities are all consequences of one basic identity which is obtained in a simple and straightforward way. It is possible to extend the results to other types of potentials as well.Report -
A deflation technique for linear systems of equations
(1994)SAM Research ReportIterative methods for solving linear systems of equations can be very efficient in a sequential or parallel computing environment if the structure of the coefficient matrix can be exploited to accelerate the convergence of the iterative process. However, for classes of problems for which suitable preconditioners cannot be found or for which the iteration scheme does not converge, iterative techniques are inappropriate. This paper proposes ...Report -
Multiquadric Pre-Wavelets on Non-Equally Spaced Centres
(1994)SAM Research ReportIn this paper, we identify univariate prewavelets on spaces spanned by translates of multiquadric functions and other radial basis functions with emnon-equally spaced/em centres (or "knots"). Although the multiquadric function and its relations are our prime examples, the theory is sufficiently broad to admit prewavelets from other radial basis function spaces as well.Report -
Knot removal with radial function interpolation
(1994)SAM Research ReportIn this note we study interpolants to $n$-variate, real valued functions from radial function spaces, \ie spaces that are spanned by radially symmetric functions $\varphi(\|\cdot - x_{j} \|_2)$ defined on $\R^n$. Here $\| \cdot \|_2$ denotes the Euclidean norm, $\varphi : \R_+ \to \R$ is a given "radial (basis) function" which we take here to be $\varphi (r) = ( r^2 + c^2)^{\beta /2}$, $-n \leq \beta < 0$, and the $\{x_j \} \subset \R^n$ ...Report -
ADVISE, Agricultural Developmental Visualisation Interactive Software Environment
(1994)SAM Research ReportThe quantum increase in computing power provided by contemporary parallel architectures offers the opportunity to confront problems of ever increasing complexity and size. With these developments new problems arise in techniques for the manipulation, transmission and display of large data sets as they occur for example in environmental modelling. The hardware and software of modern graphical display devices has the potential to enable ...Report -
SCSM - synchronous composition of sequential machines
(1994)TIK ReportThe SCSM formalism allows to define event driven synchronous systems by means of expressions formed by sum, product and restriction operators applied to non-deterministic sequential machines. Deterministic expressions are obtained through global product restrictions, which correlate transitions of non-deterministic components with states of other components. SCSM is usefull as denotation domain for synchronous system description languages, ...Report -
Protocol extension
(1994)ETH, Eidgenössische Technische Hochschule Zürich, Departement InformatikReport -
Hyperbolic Conservation Laws with Source Terms: Errors of the Shock Location
(1994)SAM Research ReportWe investigate the error of the shock location which occurs in numerical solutions of hyperbolic conservation laws with source terms. For our theoretical analysis we consider a scalar Riemann problem. We compute its solution using a splitting method. This means that in each time step the homogeneous conservation law and an ODE (modeling the source term) are solved separately. We show that the local error of the shock location can be ...Report -
A new method to approximate the volume rendering equation using wavelet bases and piecewise polynomials
(1994)ETH, Eidgenössische Technische Hochschule Zürich, Departement Informatik, Institut für InformationssystemeIn the following paper we describe a new generic method to find an approximate solution for the volume rendering equation using hierarchical, orthonormal wavelet basis functions. The approach is based on the idea that an initial volume data set can be decomposed into a pyramidal representation by means of a 3D wavelet transform. Once the wavelet function is described analytically, it is possible to approximate the volume density function. ...Report