acceleration of convergence
(0.001 seconds)
1—10 of 11 matching pages
1: 17.18 Methods of Computation
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►Method (1) can sometimes be improved by application of convergence acceleration procedures; see §3.9.
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2: 3.9 Acceleration of Convergence
§3.9 Acceleration of Convergence
… ► ►The transformation is accelerating if it is limit-preserving and if … ►It should be borne in mind that a sequence (series) transformation can be effective for one type of sequence (series) but may not accelerate convergence for another type. … ►For applications to asymptotic expansions, see §2.11(vi), Olver (1997b, pp. 540–543), and Weniger (1989, 2003).3: 15.19 Methods of Computation
4: 3.8 Nonlinear Equations
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3.8.3
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5: 3.10 Continued Fractions
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►For further information on the preceding algorithms, including convergence in the complex plane and methods for accelerating convergence, see Blanch (1964) and Lorentzen and Waadeland (1992, Chapter 3).
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6: 18.40 Methods of Computation
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►Gautschi (2004, p. 119–120) has explored the limit via the Wynn -algorithm, (3.9.11) to accelerate convergence, finding four to eight digits of precision in , depending smoothly on , for , for an example involving first numerator Legendre OP’s.
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7: Bibliography
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Shanks’ convergence acceleration transform, Padé approximants and partitions.
J. Combin. Theory Ser. A 43 (1), pp. 70–84.
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8: Bibliography W
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Nonlinear sequence transformations for the acceleration of convergence and the summation of divergent series.
Computer Physics Reports 10 (5-6), pp. 189–371.
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9: 3.5 Quadrature
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►Convergence acceleration schemes, for example Levin’s transformation (§3.9(v)), can be used when evaluating the series.
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10: 33.23 Methods of Computation
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►The power-series expansions of §§33.6 and 33.19 converge for all finite values of the radii and , respectively, and may be used to compute the regular and irregular solutions.
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►Thompson and Barnett (1985, 1986) and Thompson (2004) use combinations of series, continued fractions, and Padé-accelerated asymptotic expansions (§3.11(iv)) for the analytic continuations of Coulomb functions.
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