Work

Piecewise interlacing zeros of polynomials

Year: 2017

Type: preprint

Abstract: We introduce the concept of piecewise interlacing zeros for studying the relation of root distribution of two polynomials. The concept is pregnant with an idea of confirming the real-rootedness of polynomials in a sequence. Roughly speaking, one constructs a collection of disjoint intervals such that one may show by induction that consecutive polynomials have interlacing zeros over each of the intervals. We confirm the real-rootedness of some polynomials satisfying a recurrence with linear polynomial coefficients. This extends Gross et al.'s work where one of the polynomial coefficients is a constant.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.1712.04225

Authors: Wang, David G. L., Zhang, Jiarui

Institution: Beijing Institute of Technology

Language: English

Topic: Mathematical functions and polynomials

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Natural Science Foundation of China, Beijing Institute of Technology, Beijing Institute of Technology Research Fund Program for Young Scholars, Fundamental Research Funds for the Central Universities

Awards: G1507268232, G3136652940, G3793045529, G5461682432, G6043227419

OpenAlex ID: W2802622650

Cites: 8

Cited by:

Related to: 10