Count the Number of Complex Roots

 

Title: Count the Number of Complex Roots
Author: Wenda Li
Submission date: 2017-10-17
Abstract: Based on evaluating Cauchy indices through remainder sequences, this entry provides an effective procedure to count the number of complex roots (with multiplicity) of a polynomial within a rectangle box or a half-plane. Potential applications of this entry include certified complex root isolation (of a polynomial) and testing the Routh-Hurwitz stability criterion (i.e., to check whether all the roots of some characteristic polynomial have negative real parts).
BibTeX:
@article{Count_Complex_Roots-AFP,
  author  = {Wenda Li},
  title   = {Count the Number of Complex Roots},
  journal = {Archive of Formal Proofs},
  month   = oct,
  year    = 2017,
  note    = {\url{http://isa-afp.org/entries/Count_Complex_Roots.html},
            Formal proof development},
  ISSN    = {2150-914x},
}
License: BSD License
Depends on: Sturm_Tarski, Winding_Number_Eval
Used by: Linear_Recurrences