Abstract:The nonlinear transformations to accelerate the convergence of sequences due to Levin are considered and bounds on the errors are derived. Convergence theorems for oscillatory and some monotone sequences are proved.
- David Levin, Development of non-linear transformations of improving convergence of sequences, Internat. J. Comput. Math. 3 (1973), 371–388. MR 359261, DOI 10.1080/00207167308803075 D. LEVIN & A. SIDI (1975), "Two new classes of non-linear transformations for accelerating the convergence of infinite integrals and series." (Submitted.) A. SIDI (1977), Ph.D. Thesis, Tel Aviv University. (Hebrew) I. M. LONGMAN (1973), "On the generation of rational approximations for Laplace transform inversion with an application to viscoelasticity," SIAM J. Appl. Math., v. 24, pp. 429-440.
- M. Blakemore, G. A. Evans, and John Hyslop, Comparison of some methods for evaluating infinite range oscillatory integrals, J. Comput. Phys. 22 (1976), no. 3, 352–376. MR 455300, DOI 10.1016/0021-9991(76)90054-1 R. E. POWELL & S. M. SHAH (1972), Summability Theory and its Applications, Van Nostrand Reinhold Co., London.
- © Copyright 1979 American Mathematical Society
- Journal: Math. Comp. 33 (1979), 315-326
- MSC: Primary 65B10; Secondary 40A05, 41A25
- DOI: https://doi.org/10.1090/S0025-5718-1979-0514827-6
- MathSciNet review: 514827