Convergence properties of some nonlinear sequence transformations

Author:
Avram Sidi

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

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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.

**[1]**D. LEVIN (1973), "Development of non-linear transformations for improving convergence of sequences,"*Internat. J. Comput. Math.*, v. B3, pp. 371-388. MR**0359261 (50:11716)****[2]**D. LEVIN & A. SIDI (1975), "Two new classes of non-linear transformations for accelerating the convergence of infinite integrals and series." (Submitted.)**[3]**A. SIDI (1977), Ph.D. Thesis, Tel Aviv University. (Hebrew)**[4]**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.**[5]**M. BLAKEMORE, G. A. EVANS & J. HYSLOP (1976), "Comparison of some methods for evaluating infinite range oscillatory integrals,"*J. Computational Phys.*, v. 22, pp. 352-376. MR**0455300 (56:13539)****[6]**R. E. POWELL & S. M. SHAH (1972),*Summability Theory and its Applications*, Van Nostrand Reinhold Co., London.

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DOI:
https://doi.org/10.1090/S0025-5718-1979-0514827-6

Article copyright:
© Copyright 1979
American Mathematical Society