This 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.

The 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 ...

The Discontinuous Galerkin (DG) time-stepping method for the numerical solution of initial value ODEs is analyzed in the context of the hp-version of the Galerkin method. New a-priori error bounds explicit in the time steps and in the approximation orders are derived and it is proved that the DG method gives spectral and exponential accuracy for problems with smooth and analytic time dependence, respectively. It is further shown that ...

The 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 ...