• 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