Electronic Resource
Springer
Numerische Mathematik
82 (1999), S. 389-408
ISSN:
0945-3245
Keywords:
Mathematics Subject Classification (1991):65D30
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract. Denote by $R\left[f \right]$ the error of a Romberg quadrature rule applied to the function f. We determine approximately the constants in the bounds of the types $\left| R \left[ f \right] \right| \le \rm{const} \sup \left| f^{\left(\mu\right)} \left( x \right) \right|$ and $R \left[ f \right] \le{\rm const} {\rm Var} f^{\left(\mu-1\right)}$ $(\mu=1,2,\ldots)$ for all classical Romberg rules. By a comparison with the corresponding constants of the Gaussian rule we give the statement “The Gaussian quadrature rule is better than the Romberg method” a precise meaning.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/s002110050424
| Library |
Location |
Call Number |
Volume/Issue/Year |
Availability |
