Parallel Robust Computation of Generalized Eigenvectors of Matrix Pencils
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Publication:6336481
arXiv2003.04776MaRDI QIDQ6336481
Carl Christian Kjelgaard Mikkelsen, Mirko Myllykoski
Publication date: 10 March 2020
Abstract: 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 sequential scalar codes which compute the eigenvectors one by one. In this paper we discuss how to derive robust blocked algorithms. 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.
Has companion code repository: https://github.com/NLAFET/StarNEig
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