Granat, R.Kagstrom, B.Kressner, D.2011-05-052011-05-052011-05-05200910.1002/cpe.1386https://infoscience.epfl.ch/handle/20.500.14299/67082A parallel algorithm for reordering the eigenvalues in the real Schur form of a matrix is presented and discussed. Our novel approach adopts computational windows and delays multiple outside-window updates until each window has been completely reordered locally. By using multiple concurrent windows the parallel algorithm has a high level of concurrency, and most work is level 3 BLAS operations. The presented algorithm is also extended to the generalized real Schur form. Experimental results for ScaLAPACK-style Fortran 77 implementations on a Linux cluster confirm the efficiency and scalability of our algorithms in terms of more than 16 times of parallel speedup using 64 processors for large-scale problems. Even on a single processor our implementation is demonstrated to perform significantly better compared with the state-of-the-art serial implementation. Copyright (C) 2009 John Wiley & Sons, Ltd.parallel algorithmseigenvalue problemsinvariant subspacesdirect reorderingSylvester matrix equationscondition number estimatesAggressive Early DeflationMultishift Qr AlgorithmRegular Matrix PairSylvester EquationBlock AlgorithmsSoftwareReductiontext::journal::journal article::research article