relative precision

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11: 3.5 Quadrature

… ►When $f\in C^{\mathrm{\infty }}$, the Romberg method affords a means of obtaining high accuracy in many cases with a relatively simple adaptive algorithm. … ►(With the 20-point Gauss–Laguerre formula (§3.5(v)) the same precision can be achieved with 15 function evaluations.) …

12: Bibliography C

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Determination of $\nu$-zeros of Hankel functions. Comput. Phys. Comm. 32 (3), pp. 333–339.

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Notes:

Double-precision Fortran, maximum accuracy 7S.

External Links:

ISSN 0010-4655, Document, Code

Referenced by:

1st item.

Encodings:

BibTeX

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The Mathematical Theory of Black Holes. In General Relativity and Gravitation (Padova, 1983), pp. 5–26.

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External Links:

MathReview Entry

Referenced by:

§31.17(ii).

Encodings:

BibTeX

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Algorithm AS 310. Computing the non-central beta distribution function. Appl. Statist. 46 (1), pp. 146–156.

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Notes:

Single-precision Fortran.

External Links:

FullText, Code, ZentralBlatt

Referenced by:

2nd item.

Encodings:

BibTeX

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CRCWFN: Coupled real Coulomb wavefunctions. Comput. Phys. Comm. 79 (1), pp. 143–155.

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Notes:

Double-precision Fortran code.

External Links:

ISSN 0010-4655, Document, Code, ZentralBlatt

Referenced by:

5th item.

Encodings:

BibTeX

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Numerical evaluation of the Fermi-Dirac integrals. The Astrophysical Journal Supplement Series 71, pp. 677–699.

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Notes:

Double-precision Fortran, maximum precision 12D.

External Links:

ISSN 0067-0049, Document, Code

Referenced by:

§25.12(iii), §25.18(i), 3rd item, 3rd item.

Encodings:

BibTeX

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13: Bibliography L

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Exact computation of the $9$-$j$ symbols. Comput. Phys. Comm. 70 (3), pp. 544–556.

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Notes:

Double-precision Fortran

External Links:

ISSN 0010-4655, Document, Code, MathReview

Referenced by:

7th item.

Encodings:

BibTeX

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Algorithm 917: complex double-precision evaluation of the Wright $\omega$ function. ACM Trans. Math. Software 38 (3), pp. Art. 20, 17.

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External Links:

ISSN 0098-3500, Document, FullText, MathReview Entry, ZentralBlatt

Referenced by:

§4.13, 2nd item, §4.48(iv).

Encodings:

BibTeX

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Solutions to a generalized spheroidal wave equation: Teukolsky’s equations in general relativity, and the two-center problem in molecular quantum mechanics. J. Math. Phys. 27 (5), pp. 1238–1265.

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External Links:

ISSN 0022-2488, Document, MathReview (Basilis C. Xanthopoulos), ZentralBlatt

Referenced by:

§30.12, §31.17(ii).

Encodings:

BibTeX

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Evaluating elementary functions with guaranteed precision. Programming and Computer Software 27 (2), pp. 101–110.

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External Links:

ISSN 0361-7688, Document, MathReview Entry, ZentralBlatt

Referenced by:

§4.48(ii).

Encodings:

BibTeX

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The Principle of Relativity: A Collection of Original Memoirs on the Special and General Theory of Relativity. Methuen and Co., Ltd., London.

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Notes:

Translated from Das Relativitätsprinzip by W. Perrett and G. B. Jeffery. Reprinted by Dover Publications Inc., New York, 1952.

External Links:

MathReview, ZentralBlatt

Referenced by:

§1.6(ii).

Encodings:

BibTeX

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14: 3.6 Linear Difference Equations

… ►More precisely, assume that $f_0\ne 0$, $g_n\ne 0$ for all sufficiently large $n$, and as $n\to \mathrm{\infty }$ … ►Suppose again that $f_0\ne 0$, $w_0$ is given, and we wish to calculate $w_1,w_2,\mathrm{\dots },w_M$ to a prescribed relative accuracy $ϵ$ for a given value of $M$. … ►

3.6.9 $$\left|\frac{e_N}{p_N{p}_{N+1}}\right|\le ϵ\underset{1\le n\le M}{\min }\left|\frac{e_n}{p_n{p}_{n+1}}\right|.$$

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Symbols:

$N$: arbitrary positive integer, $ϵ$: relative accuracy, $M$: order, $p_n$: solutions and $e_n$: sequence

Referenced by:

§3.6(vi)

Permalink:

http://dlmf.nist.gov/3.6.E9

Encodings:

pMML, png, TeX

See also:

Annotations for §3.6(v), §3.6 and Ch.3

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