Polynomials, roots, and interlacing
By S. Fisk. 2006
101 citations recorded by the source corpus.
This work is divided into three parts. The first part concerns polynomials in one variable with all real roots. We consider linear transformations that preserve real rootedness, as well as matrices that preserve interlacing. The second part covers polynomials in several variables that generalize polynomials with all real roots. We introduce generating functions and use them to establish properties of a linear transformation. We also consider matrices and matrix polynomials. The third part considers polynomials with complex roots. The two main classes considered are polynomials with all roots in the left half plane (stable polynomials) and those with all roots in the lower half plane (Upper half plane polynomials). These naturally generalize to polynomials in many variables. And, of course, there is much more.
Subfields: Computational Theory and Mathematics, Numerical Analysis
View Paper: https://www.semanticscholar.org/paper/e5389d870b90004564eb9e1e163a64a8bff6a1f3
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In Computational Theory and Mathematics
- Julius Borcea
- Petter Brand'en
- David G. Wagner
- Adam W. Marcus
- Nikhil Srivastava
- Daniel A. Spielman
- Liam Solus
- Tim Netzer
In Numerical Analysis
Citations in the corpus
- Polya-Schur master theorems for circular domains and their boundaries (2006, result): “Further partial progress towards a solution to Problem 1 for = R is preliminarily reported in [ 11 ] although the same kind of remarks as in the case of Levin’s theorem apply here.”