Opuscula Math. 25, no. 2 (2005), 189-194

 
Opuscula Mathematica

Convex compact family of polynomials and its stability

Michał Góra

Abstract. Let \(P\) be a set of real polynomials of degree \(n\). Set \(P\) can be identified with some subset \(P\) of \(\mathbb{R}^n\) consists of vectors of coefficients of \(P\). If \(P\) is a polytope, then to ascertain whether the entire family of polynomials \(P\) is stable or not, it suffices to examine the stability of the one-dimensional boundary sets of \(P\). In present paper, we extend this result to convex compact polynomial families. Examples are presented to illustrate the results.

Keywords: stability, convex set of polynomials, regular set.

Mathematics Subject Classification: 26C10, 30C15, 52A20, 65L07.

Full text (pdf)

Opuscula Mathematica - cover

Cite this article as:
Michał Góra, Convex compact family of polynomials and its stability, Opuscula Math. 25, no. 2 (2005), 189-194

Download this article's citation as:
a .bib file (BibTeX),
a .ris file (RefMan),
a .enw file (EndNote)
or export to RefWorks.

In accordance with EU legislation we advise you this website uses cookies to allow us to see how the site is used. All data is anonymized.
All recent versions of popular browsers give users a level of control over cookies. Users can set their browsers to accept or reject all, or certain, cookies.