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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 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