Convergence properties of a quadrature formula of Clenshaw-Curtis type for the Gegenbauer weight function
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| 024 | 7 | 0 | |a 10.1007/s10543-014-0520-2 |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s10543-014-0520-2 | ||
| 100 | 1 | |a Smith |D H. |u Quadrature Research Centre, 2 Valleyfield Park, Terregles, DG2 9RA, Dumfries, Scotland, UK |4 aut | |
| 245 | 1 | 0 | |a Convergence properties of a quadrature formula of Clenshaw-Curtis type for the Gegenbauer weight function |h [Elektronische Daten] |c [H. Smith] |
| 520 | 3 | |a A quadrature formula of Clenshaw-Curtis type for functions of the form $$(1-x^2)^{\lambda - \frac{1}{2}}f(x)$$ ( 1 - x 2 ) λ - 1 2 f ( x ) over the interval [ $$-$$ - 1,1] exhibits a curious phenomenon when applied to certain analytic functions. As the number of points in the quadrature rule increases the error may sometimes decay to zero in two distinct stages rather than in one depending on the value of $$\lambda $$ λ . In this paper we shall derive explicit and asymptotic error formulae which describe this phenomenon. | |
| 540 | |a Springer Science+Business Media Dordrecht, 2014 | ||
| 690 | 7 | |a Gegenbauer weight function |2 nationallicence | |
| 690 | 7 | |a Clenshaw-Curtis quadrature |2 nationallicence | |
| 690 | 7 | |a Convergence rate |2 nationallicence | |
| 690 | 7 | |a Lobatto-Chebyshev quadrature |2 nationallicence | |
| 773 | 0 | |t BIT Numerical Mathematics |d Springer Netherlands |g 55/3(2015-09-01), 823-842 |x 0006-3835 |q 55:3<823 |1 2015 |2 55 |o 10543 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s10543-014-0520-2 |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s10543-014-0520-2 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 100 |E 1- |a Smith |D H. |u Quadrature Research Centre, 2 Valleyfield Park, Terregles, DG2 9RA, Dumfries, Scotland, UK |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t BIT Numerical Mathematics |d Springer Netherlands |g 55/3(2015-09-01), 823-842 |x 0006-3835 |q 55:3<823 |1 2015 |2 55 |o 10543 | ||