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Asymptotic upper bounds for the errors of Richardson extrapolation with practical application in approximate computations
Author(s) -
Soroushian Aram,
Wriggers Peter,
Farjoodi Jamshid
Publication year - 2009
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.2642
Subject(s) - richardson extrapolation , extrapolation , computation , convergence (economics) , mathematics , calculus (dental) , computer science , algorithm , statistics , medicine , dentistry , economics , economic growth
The results produced by Richardson extrapolation, though, in general, very accurate, are inexact. Numerical evaluation of this inexactness and implementation of the evaluation in practice are the objectives of this paper. First, considering linear changes of errors in the convergence plots, asymptotic upper bounds are proposed for the errors. Then, the achievement is extended to the results produced by Richardson extrapolation, and finally, an error‐controlling procedure is proposed and successfully implemented in approximate computations originated in science and engineering. Copyright © 2009 John Wiley & Sons, Ltd.