Automatic integration of a function with a parameter
- 1 November 1966
- journal article
- Published by Association for Computing Machinery (ACM) in Communications of the ACM
- Vol. 9 (11) , 804-806
- https://doi.org/10.1145/365876.365911
Abstract
Two efficient methods for automatic numerical integration are Romberg integration and adaptive Simpson integration. For integrands of the form ƒ( x ) g ( x, α ) where α is a parameter, it is shown that Romberg's method is more efficient. A FORTRAN program shows how to achieve this greater efficiency.Keywords
This publication has 19 references indexed in Scilit:
- On a modification of Romberg's algorithmBIT Numerical Mathematics, 1966
- Remark on Romberg quadratureCommunications of the ACM, 1965
- Remark on algorithm 145 [D1]: adaptive numerical integration by Simpson's ruleCommunications of the ACM, 1965
- Fehlerabschätzungen und Extrapolation mit rationalen Funktionen bei Verfahren vom Richardson-TypusNumerische Mathematik, 1964
- Bemerkungen zur Romberg-IntegrationNumerische Mathematik, 1964
- Remark on algorithm 60: Romberg integrationCommunications of the ACM, 1964
- ALGOL programmingBIT Numerical Mathematics, 1964
- Ausdehnung des Rombergschen PrinzipsNumerische Mathematik, 1963
- Algorithm 182: nonrecursive adaptive integrationCommunications of the ACM, 1963
- Algorithm 145: Adaptive numerical integration by Simpson's ruleCommunications of the ACM, 1962