TY - JOUR
T1 - On the condition of the zeros of characteristic polynomials
AU - Bürgisser, Peter
AU - Cucker, Felipe
AU - Rocha Cardozo, Elisa
PY - 2017/10
Y1 - 2017/10
N2 - 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.
AB - 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.
KW - Characteristic polynomial
KW - Condition
KW - Eigenvalues
KW - Random matrices
UR - http://www.scopus.com/inward/record.url?scp=85017445598&partnerID=8YFLogxK
UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-85017445598&origin=recordpage
U2 - 10.1016/j.jco.2017.03.004
DO - 10.1016/j.jco.2017.03.004
M3 - 21_Publication in refereed journal
VL - 42
SP - 72
EP - 84
JO - Journal of Complexity
JF - Journal of Complexity
SN - 0885-064X
ER -