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21: 9.17 Methods of Computation

… ►However, in the case of $\mathrm{Ai}\left(z\right)$ and $\mathrm{Bi}\left(z\right)$ this accuracy can be increased considerably by use of the exponentially-improved forms of expansion supplied in §9.7(v). …

22: 13.7 Asymptotic Expansions for Large Argument

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§13.7(iii) Exponentially-Improved Expansion

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23: 10.17 Asymptotic Expansions for Large Argument

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§10.17(v) Exponentially-Improved Expansions

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24: Bibliography Z

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Remark on “Algorithm 916: computing the Faddeyeva and Voigt functions”: efficiency improvements and Fortran translation. ACM Trans. Math. Softw. 42 (3), pp. 26:1–26:9.

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Notes:

Includes MATLAB and Fortran programs claiming 6S or 13S accuracy for single and double precision

External Links:

ISSN 0098-3500, Link, Document, MathReview Entry

Referenced by:

3rd item, 6th item, §7.25(iii), §7.25(vi).

Encodings:

BibTeX

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25: 6.18 Methods of Computation

… ►The attainable accuracy of the asymptotic expansions can be increased considerably by exponential improvement. …

26: 8.22 Mathematical Applications

… ►plays a fundamental role in re-expansions of remainder terms in asymptotic expansions, including exponentially-improved expansions and a smooth interpretation of the Stokes phenomenon. …

27: 10.40 Asymptotic Expansions for Large Argument

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§10.40(iv) Exponentially-Improved Expansions

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28: 3.2 Linear Algebra

… ►When the factorization (3.2.5) is available, the accuracy of the computed solution $𝐱$ can be improved with little extra computation. …We solve the system $𝐀𝛿𝐱=𝐫$ for $𝛿𝐱$, taking advantage of the existing triangular decomposition of $𝐀$ to obtain an improved solution $𝐱+𝛿𝐱$. …

29: 8.12 Uniform Asymptotic Expansions for Large Parameter

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$c_5(0)=-\frac{\mathrm{27\hspace{0.33em}45493}}{\mathrm{81517\hspace{0.33em}36320}}.$

… ►The last reference also includes an exponentially-improved version (§2.11(iii)) of the expansions (8.12.4) and (8.12.7) for $Q(a,z)$. …

30: Bibliography T

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Improved error bounds for the Liouville-Green (or WKB) approximation. J. Math. Anal. Appl. 85 (1), pp. 79–89.

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External Links:

ISSN 0022-247X, Document, MathReview (Klaus Deimling), ZentralBlatt

Referenced by:

§2.7(iii).

Encodings:

BibTeX

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Introduction to the Theory of Fourier Integrals. Third edition, Chelsea Publishing Co., New York.

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Notes:

Original edition was published in 1937 by Oxford University Press. Expanded bibliography and some improvements were made for the second and third editions.

External Links:

ISBN 0-8284-0324-4, MathReview, ZentralBlatt

Referenced by:

§1.14(i), §1.14(ii), §1.14(iv), §1.14(v), §1.14(vii), §1.8(iv), §10.22(v), §10.32(iii), §5.13.

Encodings:

BibTeX

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