Verified bounds for the determinant of real or complex point or interval matrices

Publikationstyp
Journal Article
Date Issued
2020-06
Sprache
English
Author(s)
Rump, Siegfried M.  orcid-logo
Institut
Zuverlässiges Rechnen E-19  
TORE-URI
http://hdl.handle.net/11420/4269
Journal
Journal of computational and applied mathematics  
Volume
372
Article Number
112610
Citation
Journal of Computational and Applied Mathematics (372): 112610 (2020-06)
Publisher DOI
10.1016/j.cam.2019.112610
Scopus ID
2-s2.0-85075892623
Publisher
Elsevier Science
We discuss several methods to compute a verified inclusion of the determinant of a real or complex, point or interval matrix. For point matrices, large condition number 1015, and large dimension (n=1000) still highly accurate inclusions are computed. For real interval matrices we show that any vertex may be a unique extreme point. For wide radii we show that preconditioning may widen an inclusion significantly, and Hadamard's bound may be much better.
Subjects
Classical adjoint
Determinant
Extremely ill-conditioned matrices
NP-hard
Sharp bounds
Verification methods