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 |
|---|---|
| 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 |
