On the condition of the zeros of characteristic polynomials
Research output: Journal Publications and Reviews (RGC: 21, 22, 62) › 21_Publication in refereed journal › peer-review
Author(s)
Related Research Unit(s)
Detail(s)
| Original language | English |
|---|---|
| Pages (from-to) | 72-84 |
| Journal / Publication | Journal of Complexity |
| Volume | 42 |
| Online published | 7 Apr 2017 |
| Publication status | Published - Oct 2017 |
Link(s)
Abstract
We prove that the expectation of the logarithm of the condition number of each of the zeros of the characteristic polynomial of a complex standard Gaussian matrix is
Ω (n) (the real and imaginary parts of the entries of a Gaussian matrix are independent standard Gaussian random variables). This may provide a theoretical explanation for the common practice in numerical linear algebra that advises against computing eigenvalues via root-finding for characteristic polynomials.
Ω (n) (the real and imaginary parts of the entries of a Gaussian matrix are independent standard Gaussian random variables). This may provide a theoretical explanation for the common practice in numerical linear algebra that advises against computing eigenvalues via root-finding for characteristic polynomials.
Research Area(s)
- Characteristic polynomial, Condition, Eigenvalues, Random matrices
Citation Format(s)
On the condition of the zeros of characteristic polynomials. / Bürgisser, Peter; Cucker, Felipe; Rocha Cardozo, Elisa.
In: Journal of Complexity, Vol. 42, 10.2017, p. 72-84.Research output: Journal Publications and Reviews (RGC: 21, 22, 62) › 21_Publication in refereed journal › peer-review
