Block-GMRES is an iterative method for solving nonsymmetric systems of linear equations with multiple right-hand sides. Restarting may be needed, due to orthogonalization expense or limited storage. We discuss how restarting affects convergence and the role small eigenvalues play. Then a version of restarted block-GMRES that deflates eigenvalues is presented. It is demonstrated that deflation c...

Low latency is crucial in networked multimedia applications such as on-demand streaming audio and video. In this paper, we consider the problem of restarting or resuming playback following an interactive operation such as fast forward, rewind, or indexed jump in stored on-demand video. We present two approaches to restart playback after an interactive operation, and develop algorithms to comput...

When using the Arnoldi method for approximating f(A)b, the action of a matrix function on a vector, the maximum number of iterations that can be performed is often limited by the storage requirements of the full Arnoldi basis. As a remedy, different restarting algorithms have been proposed in the literature, none of which was universally applicable, efficient, and stable at the same time. We ut...

A modification is given of the GMRES iterative method for nonsymmetric systems of linear equations. The new method deflates eigenvalues using Wu and Simon’s thick restarting approach. It has the efficiency of implicit restarting, but is simpler and does not have the same numerical concerns. The deflation of small eigenvalues can greatly improve the convergence of restarted GMRES. Also, it is de...

The distributed development and maintenance paradigm for component delivery is fraught with problems. One wants a relationship between developers and clients that is autonomous and anonymous. Yet components written in languages such as C++ require the recompilation of all dependent subsystems when a new version of a component is released. The design of Java’s binary format has side-stepped this...

We show in this text how the idea of the Implicitly Restarted Arnoldi method can be generalised to the non-symmetric Lanczos algorithm, using the two-sided Gram-Schmidt process or using a Lanczos tridiagonalisation. The implicitly restarted Lanczos method can be combined with an implicit lter. It can also be used in case of breakdown and ooers an alternative for look-ahead.

We consider a repairable system such that different completeness degrees are possible for the repair (or corrective maintenance) that go from a `minimal' up to a `complete' repair. Our question is: to what extent must the system be repaired in case of failure for the long-run availability to be optimal? The system evolves in time according to a Markov process as long as it is running, whereas t...

PURPOSE Ten percent of U.S. patients with non-small cell lung cancer experience partial radiographic responses to erlotinib or gefitinib. Despite initial regressions, these patients develop acquired resistance to erlotinib or gefitinib. In these patients, we sought to assess changes in tumor metabolism and size after stopping and restarting erlotinib or gefitinib and to determine the effect of ...