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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 -
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 -
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 -
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 -
A parallel implementation of a deflation algorithm for systems of linear equations
(1994)SAM Research ReportA general deflation technique for solving arbitrary systems of linear equations was described in Burrage et al. (1994a). This technique can be used with any iterative scheme. As the iterations proceed information is obtained about the eigenvalues of the iteration matrix which either cause slow convergence or divergence. These eigenvalues (and associated eigenvectors) are then deflated into a stiff subspace. This then leads to a coupled ...Report