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
fDate :
5/1/2006 12:00:00 AM
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;
Journal_Title :
Circuits and Systems I: Regular Papers, IEEE Transactions on
DOI :
10.1109/TCSI.2005.862180
