Condition numbers of Hessenberg companion matrices
Michael Cox; Kevin N. Vander Meulen; Adam Van Tuyl; Joseph Voskamp
Czechoslovak Mathematical Journal (2024)
- Issue: 1, page 191-209
- ISSN: 0011-4642
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topCox, Michael, et al. "Condition numbers of Hessenberg companion matrices." Czechoslovak Mathematical Journal (2024): 191-209. <http://eudml.org/doc/299216>.
@article{Cox2024,
abstract = {The Fiedler matrices are a large class of companion matrices that include the well-known Frobenius companion matrix. The Fiedler matrices are part of a larger class of companion matrices that can be characterized by a Hessenberg form. We demonstrate that the Hessenberg form of the Fiedler companion matrices provides a straight-forward way to compare the condition numbers of these matrices. We also show that there are other companion matrices which can provide a much smaller condition number than any Fiedler companion matrix. We finish by exploring the condition number of a class of matrices obtained from perturbing a Frobenius companion matrix while preserving the characteristic polynomial.},
author = {Cox, Michael, Vander Meulen, Kevin N., Van Tuyl, Adam, Voskamp, Joseph},
journal = {Czechoslovak Mathematical Journal},
keywords = {companion matrix; Fiedler companion matrix; condition number; generalized companion matrix},
language = {eng},
number = {1},
pages = {191-209},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Condition numbers of Hessenberg companion matrices},
url = {http://eudml.org/doc/299216},
year = {2024},
}
TY - JOUR
AU - Cox, Michael
AU - Vander Meulen, Kevin N.
AU - Van Tuyl, Adam
AU - Voskamp, Joseph
TI - Condition numbers of Hessenberg companion matrices
JO - Czechoslovak Mathematical Journal
PY - 2024
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
IS - 1
SP - 191
EP - 209
AB - The Fiedler matrices are a large class of companion matrices that include the well-known Frobenius companion matrix. The Fiedler matrices are part of a larger class of companion matrices that can be characterized by a Hessenberg form. We demonstrate that the Hessenberg form of the Fiedler companion matrices provides a straight-forward way to compare the condition numbers of these matrices. We also show that there are other companion matrices which can provide a much smaller condition number than any Fiedler companion matrix. We finish by exploring the condition number of a class of matrices obtained from perturbing a Frobenius companion matrix while preserving the characteristic polynomial.
LA - eng
KW - companion matrix; Fiedler companion matrix; condition number; generalized companion matrix
UR - http://eudml.org/doc/299216
ER -
References
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