scholarly journals Asymptotically extremal polynomials with respect to varying weights and application to Sobolev orthogonality

2008 ◽  
Vol 346 (2) ◽  
pp. 480-488 ◽  
Author(s):  
C. Díaz Mendoza ◽  
R. Orive ◽  
H. Pijeira Cabrera
Keyword(s):  
Extremal Polynomials ◽  
Sobolev Orthogonality

scholarly journals Caustics of Poncelet Polygons and Classical Extremal Polynomials

2019 ◽  
Vol 24 (1) ◽  
pp. 1-35 ◽  
Author(s):  
Vladimir Dragović ◽  
Milena Radnović
Keyword(s):  
Extremal Polynomials ◽  
Poncelet Polygons

On the Widom factors for Lp extremal polynomials

2020 ◽  
Vol 259 ◽  
pp. 105480
Author(s):  
Gökalp Alpan ◽  
Maxim Zinchenko
Keyword(s):  
Extremal Polynomials

Polynomials With {0, +1, -1} Coefficients and a Root Close to a Given Point

1997 ◽  
Vol 49 (5) ◽  
pp. 887-915 ◽  
Author(s):  
Peter Borwein ◽  
Christopher Pinner
Keyword(s):  
Algebraic Number ◽  
Real Root ◽  
Small Degree ◽  
Pisot Number ◽  
Roots Of Unity ◽  
Best Approximations ◽  
Rate Of Approximation ◽  
Root Of Unity ◽  
Extremal Polynomials ◽  
Image Position

AbstractFor a fixed algebraic number α we discuss how closely α can be approximated by a root of a {0, +1, -1} polynomial of given degree. We show that the worst rate of approximation tends to occur for roots of unity, particularly those of small degree. For roots of unity these bounds depend on the order of vanishing, k, of the polynomial at α.In particular we obtain the following. Let BN denote the set of roots of all {0, +1, -1} polynomials of degree at most N and BN(α k) the roots of those polynomials that have a root of order at most k at α. For a Pisot number α in (1, 2] we show thatand for a root of unity α thatWe study in detail the case of α = 1, where, by far, the best approximations are real. We give fairly precise bounds on the closest real root to 1. When k = 0 or 1 we can describe the extremal polynomials explicitly.

scholarly journals Logarithmic asymptotics of contracted Sobolev extremal polynomials on the real line

2006 ◽  
Vol 143 (1) ◽  
pp. 62-73 ◽  
Author(s):  
G. López Lagomasino ◽  
F. Marcellán Español ◽  
H. Pijeira Cabrera
Keyword(s):  
Real Line ◽  
The Real ◽  
Extremal Polynomials ◽  
Logarithmic Asymptotics

scholarly journals Linear interpolation and Sobolev orthogonality

2009 ◽  
Vol 161 (1) ◽  
pp. 35-48 ◽  
Author(s):  
Samuel G. Moreno ◽  
Esther M. García-Caballero
Keyword(s):  
Linear Interpolation ◽  
Sobolev Orthogonality
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