## The $d_2$-transformation for infinite double series and the $D_2$-transformation for infinite double integrals

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- by Chen Greif and David Levin PDF
- Math. Comp.
**67**(1998), 695-714 Request permission

## Abstract:

New transformations for accelerating the convergence of infinite double series and infinite double integrals are presented. These transformations are generalizations of the univariate $d$- and $D$-transformations. The $D_2$-transformation for infinite double integrals is efficient if the integrand satisfies a p.d.e. of a certain type. Similarly, the $d_2$-transformation for double series works well for series whose terms satisfy a difference equation of a certain type. In both cases, the application of the transformation does not require an explicit knowledge of the differential or the difference equation. Asymptotic expansions for the remainders in the infinite double integrals and series are derived, and nonlinear transformations based upon these expansions are presented. Finally, numerical examples which demonstrate the efficiency of these transformations are given.## References

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## Additional Information

**Chen Greif**- Affiliation: School of Mathematical Sciences, Tel-Aviv University, Tel-Aviv 69978, Israel
- Address at time of publication: Department of Mathematics, University of British Columbia, Vancouver, B.C., Canada V6T-1Z2
- MR Author ID: 622883
- Email: greif@math.ubc.ca
**David Levin**- Affiliation: School of Mathematical Sciences, Tel-Aviv University, Tel-Aviv 69978, Israel
- Email: levin@math.tau.ac.il
- Received by editor(s): November 21, 1995
- Received by editor(s) in revised form: July 19, 1996, and January 8, 1997
- © Copyright 1998 American Mathematical Society
- Journal: Math. Comp.
**67**(1998), 695-714 - MSC (1991): Primary 65B10; Secondary 40B05, 65D30
- DOI: https://doi.org/10.1090/S0025-5718-98-00955-7
- MathSciNet review: 1464144