Crouzeix's conjecture holds for a subclass of tridiagonal 3x3 matrices

Christer Glader; Mikael Kurula; Mikael Lindström

Crouzeix's conjecture holds for a subclass of tridiagonal 3x3 matrices

Christer Glader, Mikael Kurula, Mikael Lindström

Mathematics

Tutkimustuotos: Kirja/lehti/raportti › Tutkimusraportti › Ammatillinen

Abstrakti

M. Crouzeix formulated the following conjecture in (Integral EquationsOperator Theory 48, 2004, 461--477): For every square matrix A and everypolynomial p,

∥p(A)∥≤2maxz∈W(A)|p(z)|, where W(A) is thenumerical range of A. We show that the conjecture holds for tridiagonal3×3 matrices ⎡⎣⎢ac0bac0ba⎤⎦⎥,a,b,c∈C, with constant diagonals, even if anynumber of off-diagonal elements should be set to zero. We also extend the mainresult of D. Choi in (Linear Algebra Appl. 438, 3247--3257) slightly.

Alkuperäiskieli	Ei tiedossa
Kustantaja	arXiv.org
Tila	Julkaistu - 2017
OKM-julkaisutyyppi	D4 Julkaistut kehitykset tai tutkimusraportit tai tutkimukset

Pääsy asiakirjaan

https://arxiv.org/abs/1701.01365v1

Viittausmuodot

@book{8d209b8116c44c3a97c40f62350dc66b,

title = "Crouzeix's conjecture holds for a subclass of tridiagonal 3x3 matrices",

abstract = "M. Crouzeix formulated the following conjecture in (Integral EquationsOperator Theory 48, 2004, 461--477): For every square matrix A and everypolynomial p, ∥p(A)∥≤2maxz∈W(A)|p(z)|, where W(A) is thenumerical range of A. We show that the conjecture holds for tridiagonal3×3 matrices ⎡⎣⎢ac0bac0ba⎤⎦⎥,a,b,c∈C, with constant diagonals, even if anynumber of off-diagonal elements should be set to zero. We also extend the mainresult of D. Choi in (Linear Algebra Appl. 438, 3247--3257) slightly.",

author = "Christer Glader and Mikael Kurula and Mikael Lindstr{\"o}m",

year = "2017",

language = "Odefinierat/ok{\"a}nt",

publisher = "arXiv.org",

}

TY - BOOK

T1 - Crouzeix's conjecture holds for a subclass of tridiagonal 3x3 matrices

AU - Glader, Christer

AU - Kurula, Mikael

AU - Lindström, Mikael

PY - 2017

Y1 - 2017

N2 - M. Crouzeix formulated the following conjecture in (Integral EquationsOperator Theory 48, 2004, 461--477): For every square matrix A and everypolynomial p, ∥p(A)∥≤2maxz∈W(A)|p(z)|, where W(A) is thenumerical range of A. We show that the conjecture holds for tridiagonal3×3 matrices ⎡⎣⎢ac0bac0ba⎤⎦⎥,a,b,c∈C, with constant diagonals, even if anynumber of off-diagonal elements should be set to zero. We also extend the mainresult of D. Choi in (Linear Algebra Appl. 438, 3247--3257) slightly.

AB - M. Crouzeix formulated the following conjecture in (Integral EquationsOperator Theory 48, 2004, 461--477): For every square matrix A and everypolynomial p, ∥p(A)∥≤2maxz∈W(A)|p(z)|, where W(A) is thenumerical range of A. We show that the conjecture holds for tridiagonal3×3 matrices ⎡⎣⎢ac0bac0ba⎤⎦⎥,a,b,c∈C, with constant diagonals, even if anynumber of off-diagonal elements should be set to zero. We also extend the mainresult of D. Choi in (Linear Algebra Appl. 438, 3247--3257) slightly.

M3 - Beställd rapport

BT - Crouzeix's conjecture holds for a subclass of tridiagonal 3x3 matrices

PB - arXiv.org

ER -