Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Remote Access
Green Open Access
Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Chebyshev-type quadrature and partial sums of the exponential series


Author: Arno Kuijlaars
Journal: Math. Comp. 64 (1995), 251-263
MSC: Primary 65D32; Secondary 41A55
MathSciNet review: 1250771
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Chebyshev-type quadrature for the weight functions

$\displaystyle {w_a}(t) = \frac{{1 - at}}{{\pi \sqrt {1 - {t^2}} }},\quad - 1 < t < 1,\quad - 1 < a < 1,$

is related to a problem concerning partial sums of the exponential series, namely the problem to extend the nth partial sum to a polynomial of degree 2N having all zeros on the circle $ \vert z\vert = \vert a\vert N$. Using this connection, we show that the minimal number N of nodes needed for Chebyshev-type quadrature of degree n for $ {w_a}(t)$ satisfies an inequality $ {C_1}n \leq N \leq {C_2}n$ with positive constants $ {C_1},{C_2}$. As an application we prove that the minimal number N of nodes for Chebyshev-type quadrature of degree n on a torus embedded in $ {{\mathbf{R}}^3}$ satisfies an inequality $ {C_1}{n^2} \leq N \leq {C_2}{n^2}$.

References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65D32, 41A55

Retrieve articles in all journals with MSC: 65D32, 41A55


Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1995-1250771-6
PII: S 0025-5718(1995)1250771-6
Keywords: Chebyshev-type quadrature, partial sums, distribution of zeros, multidimensional quadrature
Article copyright: © Copyright 1995 American Mathematical Society



Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia