Parallel Robust Computation of Generalized Eigenvectors of Matrix Pencils

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 12043)


In this paper we consider the problem of computing generalized eigenvectors of a matrix pencil in real Schur form. In exact arithmetic, this problem can be solved using substitution. In practice, substitution is vulnerable to floating-point overflow. The robust solvers xtgevc in LAPACK prevent overflow by dynamically scaling the eigenvectors. These subroutines are scalar and sequential codes which compute the eigenvectors one by one. In this paper, we discuss how to derive robust algorithms which are blocked and parallel. The new StarNEig library contains a robust task-parallel solver Zazamoukh which runs on top of StarPU. Our numerical experiments show that Zazamoukh achieves a super-linear speedup compared with dtgevc for sufficiently large matrices.


Generalized eigenvectors Overflow protection Task-parallelism 



This work is part of a project (NLAFET) that has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No 671633. This work was supported by the Swedish strategic research programme eSSENCE. We thank the High Performance Computing Center North (HPC2N) at Umeå University for providing computational resources and valuable support during test and performance runs.


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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Department of Computing Science and HPC2NUmeå UniversityUmeåSweden

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