Parallel Robust Computation of Generalized Eigenvectors of Matrix Pencils
| Autor: | Mikkelsen, Carl Christian Kjelgaard, Myllykoski, Mirko |
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| Rok vydání: | 2020 |
| Předmět: | |
| Zdroj: | LNCS 12043 (2020) 58-69 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/978-3-030-43229-4_6 |
| Popis: | 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. Comment: This manuscript was accepted to 13th International Conference on Parallel Processing and Applied Mathematics (PPAM2019), Bialystok, Poland, September 8-11, 2019. The final authenticated version is available online at https://doi.org/10.1007/978-3-030-43229-4_6 (DOI valid from May 8, 2020 onward). First author's first name is "Carl Christian" and last name "Kjelgaard Mikkelsen" |
| Databáze: | arXiv |
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