In this paper, the eigenvalue distribution of a family of relaxed mixed constraint preconditioner (RMCP) for the generalized saddle point problems is discussed in detail. Most of the bounds developed improve those appeared in previously published work.

We investigate methods for efficiently solving a complex symmetric (non-Hermitian) generalized eigenvalue problem (EVP) Ax = λBx in parallel. An evaluation featuring up to 1024 CPU-cores evidences encouraging runtime behavior.

The eigenvalue shift technique is the most well-known and fundamental tool for matrix computations. Applications include the search of eigeninformation, the acceleration of numerical algorithms, the study of Google’s PageRank. The shift strategy arises from the concept investigated by Brauer [1] for changing the value of an eigenvalue of a matrix to the desired one, while keeping the remaining ...

1. Page 2741, caption of Fig. 2: three occurrences of ‘‘commutator’’ instead of ‘‘commutor’’, i.e. the caption should read Fig. 2. Eigenvalue decomposition of the commutor for the CDFT: (a) sorted eigenvalues of the commutor T1 for N 1⁄4 128. (b) Selected symmetric and skew-symmetric eigenvectors of the commutor for k 1⁄4 0,1, 2, 3. 2. Page 2743, fourth sentence after Eq. (14): ‘‘commutator’’ i...