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1: 3.9 Acceleration of Convergence

§3.9 Acceleration of Convergence

… ► ►The transformation is accelerating if it is limit-preserving and if … ►This transformation is accelerating if $\{s_n\}$ is a linearly convergent sequence, i. … ►For applications to asymptotic expansions, see §2.11(vi), Olver (1997b, pp. 540–543), and Weniger (1989, 2003).

2: 17.18 Methods of Computation

… ►Method (1) can sometimes be improved by application of convergence acceleration procedures; see §3.9. …

3: 15.19 Methods of Computation

… ►Moreover, it is also possible to accelerate convergence by appropriate choice of $z_0$. …

4: 33.23 Methods of Computation

… ►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. …

5: 3.8 Nonlinear Equations

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3.8.3

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Symbols:

$\zeta$: fixed point

A&S Ref:

3.9.2

Referenced by:

§3.8(i)

Permalink:

http://dlmf.nist.gov/3.8.E3

Encodings:

pMML, png, TeX

See also:

Annotations for §3.8(i), §3.8 and Ch.3

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6: 36.13 Kelvin’s Ship-Wave Pattern

… ►Then with $g$ denoting the acceleration due to gravity, the wave height is approximately given by …

7: Bibliography

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Study of nuclear structure by electromagnetic excitation with accelerated ions. Rev. Mod. Phys. 28, pp. 432–542.

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External Links:

ISSN 0034-6861, Document, MathReview, ZentralBlatt

Referenced by:

§33.22(ii).

Encodings:

BibTeX

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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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External Links:

ISSN 0097-3165, Document, MathReview (Kenneth A. Jukes), ZentralBlatt

Referenced by:

§17.18.

Encodings:

BibTeX

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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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External Links:

Document

Referenced by:

§2.11(vi), §3.9(v), §3.9(vi).

Encodings:

BibTeX

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9: 3.10 Continued Fractions

… ►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). …

10: 18.40 Methods of Computation

… ►Gautschi (2004, p. 119–120) has explored the $\epsilon \to 0^{+}$ limit via the Wynn $\epsilon$-algorithm, (3.9.11) to accelerate convergence, finding four to eight digits of precision in $w(x)$, depending smoothly on $x^{\prime }$, for $N\approx 4000$, for an example involving first numerator Legendre OP’s. …