DocumentCode
929998
Title
Two-variable polynomials: intersecting zeros and stability
Author
Geronimo, Jeffrey S. ; Woerdeman, Hugo J.
Author_Institution
Sch. of Math., Georgia Inst. of Technol., Atlanta, GA, USA
Volume
53
Issue
5
fYear
2006
fDate
5/1/2006 12:00:00 AM
Firstpage
1130
Lastpage
1139
Abstract
In order to construct two-variable polynomials with a certain zero behavior, the notion of intersecting zeros is studied. We show that generically two-variable polynomials have a finite set of intersecting zeros, and give an algorithm on how to construct a polynomial with the desired intersecting zeros. Relations with the Cayley-Bacharach theorem are addressed. In addition, we will also address the case when stable polynomials are sought.
Keywords
matrix algebra; numerical stability; polynomial matrices; Cayley-Bacharach theorem; Fejer-Riesz factorization; Schur-Cohn theorem; intersecting zeros; resultant valued matrix polynomials; spectral factorization; Density functional theory; Filters; Mathematics; Polynomials; Prediction theory; Stability; Terminology; Cayley–Bacharach; FejÉr–Riesz factorization; Intersecting zeros; Schur–Cohn; resultant valued matrix polynomials; spectral factorization; stability;
fLanguage
English
Journal_Title
Circuits and Systems I: Regular Papers, IEEE Transactions on
Publisher
ieee
ISSN
1549-8328
Type
jour
DOI
10.1109/TCSI.2005.862180
Filename
1629251
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