arXiv Open Access 2020

Parallel Robust Computation of Generalized Eigenvectors of Matrix Pencils

Carl Christian Kjelgaard Mikkelsen Mirko Myllykoski

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Abstrak

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.

Topik & Kata Kunci

cs.MS cs.DC math.NA

Penulis (2)

Carl Christian Kjelgaard Mikkelsen

Mirko Myllykoski

Format Sitasi

APA MLA BibTeX

Mikkelsen, C.C.K., Myllykoski, M. (2020). Parallel Robust Computation of Generalized Eigenvectors of Matrix Pencils. https://arxiv.org/abs/2003.04776

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Informasi Jurnal

Tahun Terbit: 2020
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓