The Faddeev-LeVerrier algorithm and the Pfaffian
- We adapt the Faddeev-LeVerrier algorithm for the computation of characteristic polynomials to the computation of the Pfaffian of a skew-symmetric matrix. This yields a very simple, easy to implement and parallelize algorithm of computational cost O(n(beta+1)) where nis the size of the matrix and O(n(beta)) is the cost of multiplying n x n-matrices, beta is an element of [2, 2.37286). We compare its performance to that of other algorithms and show how it can be used to compute the Euler form of a Riemannian manifold using computer algebra.
Author details: | Christian BärORCiDGND |
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DOI: | https://doi.org/10.1016/j.laa.2021.07.023 |
ISSN: | 0024-3795 |
ISSN: | 1873-1856 |
Title of parent work (English): | Linear algebra and its applications |
Publisher: | Elsevier |
Place of publishing: | New York |
Publication type: | Article |
Language: | English |
Date of first publication: | 2021/08/05 |
Publication year: | 2021 |
Release date: | 2023/01/23 |
Tag: | Characteristic polynomial; Determinant; Gauss-Bonnet-Chern; Pfaffian; theorem |
Volume: | 630 |
Number of pages: | 17 |
First page: | 39 |
Last Page: | 55 |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
DDC classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
Peer review: | Referiert |