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Restarted GMRES preconditioned by deflation
(1994)SAM Research ReportThis paper presents a new preconditioning technique for solving linear systems. It is based on an invariant subspace approximation for the restarted GMRES algorithm. It uses the flexible GMRES scheme by designing a new preconditioning after each restart. Numerical examples show that this approach may converge almost as fast as full-GMRES at a, possibly, much lower cost.Report -
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Circuits in Power Electronics
(1994)SAM Research ReportThe dynamics of circuits in power electronics may often be modelled by means of systems of linear differential equations with piecewise constant coefficients and sinusoidal inhomogeneities. The Static Var (Volt-Ampere reactive) Compensator (SVC, a device for power network control) is a representative example. Initial value problems of this type may be handled by means of the matrix exponential, whereas the construction of periodic solutions ...Report -
The implementation of a Generalized Cross Validation algorithm using deflation techniques for linear systems
(1994)SAM Research ReportThe fitting of a thin plate smoothing spline to noisy data using the method of minimizing the Generalized Cross Validation (GCV) function is computationally intensive involving the repeated solution of sets of linear systems of equations as part of a minimization routine. In the case of a data set of more than a few hundred points, implementation on a workstation can become unrealistic and it is then desirable to exploit high performance ...Report -
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