The joint spectral radius is pointwise Hölder continuous

Jeremias Epperlein; Fabian Wirth

doi:10.1016/j.laa.2024.09.016

The joint spectral radius is pointwise Hölder continuous

Jeremias Epperlein
, Fabian Wirth

Research output: Contribution to journal › Article › peer-review

Abstract

We show that the joint spectral radius is pointwise Hölder continuous. In addition, the joint spectral radius is locally Hölder continuous for ε-inflations. In the two-dimensional case, local Hölder continuity holds on the matrix sets with positive joint spectral radius.

Original language	English
Pages (from-to)	92-122
Number of pages	31
Journal	Linear Algebra and Its Applications
Volume	704
DOIs	https://doi.org/10.1016/j.laa.2024.09.016
State	Published - 1 Jan 2025
Externally published	Yes

Keywords

Extremal norm
Hölder continuity
Joint spectral radius

ASJC Scopus subject areas

Algebra and Number Theory
Numerical Analysis
Geometry and Topology
Discrete Mathematics and Combinatorics

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10.1016/j.laa.2024.09.016

Cite this

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title = "The joint spectral radius is pointwise H{\"o}lder continuous",

abstract = "We show that the joint spectral radius is pointwise H{\"o}lder continuous. In addition, the joint spectral radius is locally H{\"o}lder continuous for ε-inflations. In the two-dimensional case, local H{\"o}lder continuity holds on the matrix sets with positive joint spectral radius.",

keywords = "Extremal norm, H{\"o}lder continuity, Joint spectral radius",

author = "Jeremias Epperlein and Fabian Wirth",

note = "Publisher Copyright: {\textcopyright} 2024 The Author(s)",

year = "2025",

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doi = "10.1016/j.laa.2024.09.016",

language = "English",

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journal = "Linear Algebra and Its Applications",

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T1 - The joint spectral radius is pointwise Hölder continuous

AU - Epperlein, Jeremias

AU - Wirth, Fabian

PY - 2025/1/1

Y1 - 2025/1/1

N2 - We show that the joint spectral radius is pointwise Hölder continuous. In addition, the joint spectral radius is locally Hölder continuous for ε-inflations. In the two-dimensional case, local Hölder continuity holds on the matrix sets with positive joint spectral radius.

AB - We show that the joint spectral radius is pointwise Hölder continuous. In addition, the joint spectral radius is locally Hölder continuous for ε-inflations. In the two-dimensional case, local Hölder continuity holds on the matrix sets with positive joint spectral radius.

KW - Extremal norm

KW - Hölder continuity

KW - Joint spectral radius

UR - https://www.scopus.com/pages/publications/85206526291

U2 - 10.1016/j.laa.2024.09.016

DO - 10.1016/j.laa.2024.09.016

M3 - Article

AN - SCOPUS:85206526291

SN - 0024-3795

VL - 704

SP - 92

EP - 122

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

ER -

The joint spectral radius is pointwise Hölder continuous

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

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