Several Krylov subspace iterative methods have been proposed for the approximation of the solution of general non-symmetric linear systems. Odir is such a method. Here we study the restarted version of Odir for non-symmetric inde nite linear systems and we prove convergence under certain conditions on the matrix of coe cients. These results hold for all the restarted Krylov methods equivalent t...

In many physical situations, a few specific eigenvalues of a large sparse generalized eigenvalue problem Ax = λBx are needed. If exact linear solves with A−σB are available, implicitly restarted Arnoldi with purification is a common approach for problems where B is positive semidefinite. In this paper, a new approach based on implicitly restarted Arnoldi will be presented that avoids most of th...

Agents targeting vascular endothelial growth factor (VEGF) represent active drugs in treating patients with advanced renal cell carcinoma (RCC). Studies have shown that sunitinib and axitinib can be associated with cardiac toxicity. Whether these agents should be restarted in patients who experience cardiac ischemia remains uncertain. Here, we present three patients with metastatic RCC who rest...

Since evolutionary algorithms make heavy use of randomness it is typically the case that they succeed only with some probability. In cases of failure often the algorithm is restarted. Of course, it is desirable that the point of time when the current run is considered to be a failure and therefore the algorithm is stopped and restarted is determined by the algorithm itself rather than by the us...

Abstract With the recent realization of exascale performance by Oak Ridge National Laboratory’s Frontier supercomputer, reducing communication in kernels like QR factorization has become even more imperative. Low-synchronization Gram-Schmidt methods, first introduced Świrydowicz et al. ( Numer. Lin. Alg. Appl. 28(2):e2343, 2020), have been shown to improve scalability Arnoldi method high-perfor...