Asymptotic Error Formulae for Numerical Quadrature |
| |
Authors: | OSBORNE M R |
| |
Institution: |
Computer Centre, Australian National University
|
| |
Abstract: | A method, due to Fox, is used to derive asymptotic error formulaefor numerical procedures having the form (z+h, h). (z,h)= (f,z,h).These procedures correspond to numerical quadrature for theintegrand (![{partial}](http://imamat.oxfordjournals.org/math/part.gif) / h)(f,z,0)and compact expressions are given for determiningthe order of convergence as h 0, and the leading term in theerror. It is shown that a natural generalization of the Euler-Maclaurinexpansion is available. These results are applied to the particularcase
where the Pt are polynomials in the differentiation operator.A related interpolation problem is also studied, and it is shownthat in certain cases higher order quadrature formulae are possiblewhen this interpolation problem is not poised. |
| |
Keywords: | |
本文献已被 Oxford 等数据库收录! |
|