𝔖 Bobbio Scriptorium
✦   LIBER   ✦

On the largest polytope of polynomials with a precise number of distinct real zeros

✍ Scribed by C.B. Soh

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
353 KB
Volume
265
Category
Article
ISSN
0024-3795

No coin nor oath required. For personal study only.

✦ Synopsis

This paper presents a procedure to construct the largest polytope of polynomials with every polynomial having a precise number of distinct real zeros in a specific real line segment. This polytope can be specified from the zeros of a finite number of polynomials.

πŸ“œ SIMILAR VOLUMES

Zeros of orthogonal polynomials on the r
Zeros of orthogonal polynomials on the real line
✍ Sergey A Denisov; Barry Simon πŸ“‚ Article πŸ“… 2003 πŸ› Elsevier Science 🌐 English βš– 144 KB

Let p n Γ°xÞ be the orthonormal polynomials associated to a measure dm of compact support in R: If EesuppΓ°dmÞ; we show there is a d40 so that for all n; either p n or p nΓΎ1 has no zeros in Γ°E Γ€ d; E ΓΎ dÞ: If E is an isolated point of suppΓ°mÞ; we show there is a d so that for all n; either p n or p nΓΎ

On expected number of real zeros of a ra
On expected number of real zeros of a random hyperbolic polynomial with dependent coefficients
✍ Mina Ketan Mahanti πŸ“‚ Article πŸ“… 2009 πŸ› Elsevier Science 🌐 English βš– 388 KB

The asymptotic estimate of the expected number of real zeros of the random hyperbolic . . , y n (Ο‰) are independent and normally distributed random variables with mean zero and variance one. We have considered here the case when the random coefficients are dependent and proved that the expected num