scholarly journals Corrigendum to “Rate of Approximation for Modified Lupaş-Jain-Beta Operators”

2021 ◽  
Vol 2021 ◽  
pp. 1-1
Author(s):  
M. Qasim ◽  
Asif Khan ◽  
Zaheer Abbas ◽  
Princess Raina ◽  
Qing-Bo Cai
Keyword(s):  
Rate Of Approximation

Smoothness of functions and rate of approximation

2008 ◽  
Vol 41 (4) ◽  
pp. 318-323
Author(s):  
O. V. Sil’vanovich ◽  
N. A. Shirokov
Keyword(s):  
Rate Of Approximation

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.

EDGE ELEMENT COMPUTATION OF MAXWELL'S EIGENVALUES ON GENERAL QUADRILATERAL MESHES

2006 ◽  
Vol 16 (02) ◽  
pp. 265-273 ◽  
Author(s):  
DANIELE BOFFI ◽  
FUMIO KIKUCHI ◽  
JOACHIM SCHÖBERL
Keyword(s):  
Optimal Rate ◽  
Projection Technique ◽  
Integration Procedure ◽  
Edge Element ◽  
Edge Elements ◽  
Rate Of Approximation ◽  
Quadrilateral Meshes ◽  
Reduced Integration ◽  
Element Computation

Recent results prove that Nédélec edge elements do not achieve optimal rate of approximation on general quadrilateral meshes. In particular, lowest order edge elements provide stable but non-convergent approximation of Maxwell's eigenvalues. In this paper we analyze a modification of standard edge element that restores the optimality of the convergence. This modification is based on a projection technique that can be interpreted as a reduced integration procedure.

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