Bounds for the zeros of polynomials from eigenvalues and singular values of some companion matrices

Linden, Hansjörg

doi:10.1016/s0024-3795(97)00254-1

Cited by 24 publications

(9 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A bound for the zeros of p can be obtained from the inequalities (14) and (19). However, using the spectral mapping theorem, we conclude that if z is any zero of p, then |z| ≤ C(p) 2 1/2 .…”

Section: Z| ≤ W(c(p)) (14)mentioning

confidence: 99%

A numerical radius inequality and an estimate for the numerical radius of the Frobenius companion matrix

Kittaneh

2003

Studia Math.

204

View full text Add to dashboard Cite

show abstract

Section: Z| ≤ W(c(p)) (14)mentioning

confidence: 99%

A numerical radius inequality and an estimate for the numerical radius of the Frobenius companion matrix

Kittaneh

2003

Studia Math.

204

View full text Add to dashboard Cite

show abstract

“…By considering the imaginary part of C(p), an analysis similar to that used in deriving the bounds (12) enables us to obtain analogous bounds for the imaginary parts of the zeros of p. These bounds, when combined with (12), describe a rectangle that contains all the zeros of p. Related rectangles have been described in [11,Theorem 3].…”

Section: Resultsmentioning

confidence: 99%

Bounds and a majorization for the real parts of the zeros of polynomials

Kittaneh

2006

Proc. Amer. Math. Soc.

View full text Add to dashboard Cite

show abstract

“…This idea is used in, e.g., [1], [3], [5], [11], [12], and [16], to name just a few references from the vast literature on this subject.…”

Section: Companion Matrices and Gershgorin's Theoremmentioning

confidence: 99%

Modified Gershgorin Disks for Companion Matrices

Melman¹

2012

SIAM Rev.

View full text Add to dashboard Cite

Abstract. All the zeros of a polynomial are contained in the union of Gershgorin disks derived from its companion matrix, a consequence of Gershgorin's theorem. However, this theorem does not exploit the structure of the companion matrix. We will use this structure to obtain smaller zero inclusion regions, thereby providing some nonstandard results to accompany and illustrate this frequently covered topic in numerical and matrix analysis.

show abstract

Bounds for the zeros of polynomials from eigenvalues and singular values of some companion matrices

Cited by 24 publications

References 18 publications

A numerical radius inequality and an estimate for the numerical radius of the Frobenius companion matrix

A numerical radius inequality and an estimate for the numerical radius of the Frobenius companion matrix

Bounds and a majorization for the real parts of the zeros of polynomials

Modified Gershgorin Disks for Companion Matrices

Contact Info

Product

Resources

About