Remez second algorithm

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21: Bibliography H

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Fast Hankel transform algorithm. IEEE Trans. Acoust. Speech Signal Process. 32 (3), pp. 666–671.

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External Links:

ISSN 0096-3518, FullText, ZentralBlatt

Referenced by:

§10.74(vii).

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Algorithm 55: Complete elliptic integral of the first kind. Comm. ACM 4 (4), pp. 180.

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Notes:

Includes Algol program, maximum accuracy 8D. For certification see same journal 6 (1966), pp. 166–167

External Links:

ISSN 0001-0782, Document

Referenced by:

§19.39(ii).

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Algorithm 56: Complete elliptic integral of the second kind. Comm. ACM 4 (4), pp. 180–181.

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Notes:

Includes Algol program, maximum accuracy 8D. For certification see same journal 9 (1966), p. 12

External Links:

ISSN 0001-0782, Document

Referenced by:

§19.39(ii).

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Algorithm 442: Normal deviate. Comm. ACM 16 (1), pp. 51–52.

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Notes:

Includes Algol program, minimum accuracy 24D.

External Links:

ISSN 0001-0782, Document

Referenced by:

§7.25(ii).

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Algorithm AS66: The normal integral. Appl. Statist. 22 (3), pp. 424–427.

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Notes:

Double-precision Fortran, maximum accuracy 12D.

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FullText, Code

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5th item.

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22: Bibliography P

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Algorithm 385: Exponential integral $\mathrm{Ei}(x)$ . Comm. ACM 13 (7), pp. 446–447.

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Notes:

Includes Fortran code, maximum accuracy 20D. For certification and remarks see same journal v. 13 (1970), pp. 448–449 and p. 750; v. 15 (1972), p. 1074.

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ISSN 0001-0782, Document

Referenced by:

§6.21(ii).

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Sur les équations différentielles du second ordre à points critiques fixès. C.R. Acad. Sc. Paris 143, pp. 1111–1117.

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ZentralBlatt

Referenced by:

§32.2(iv).

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Algorithm 28. Algorithm for the computation of Bessel function integrals. J. Comput. Appl. Math. 11 (1), pp. 119–137.

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ISSN 0377-0427, Document, ZentralBlatt

Referenced by:

§10.77(ix).

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Algorithm 680: Evaluation of the complex error function. ACM Trans. Math. Software 16 (1), pp. 47.

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Notes:

Single-precision Fortran, maximum accuracy 14S.

External Links:

ISSN 0098-3500, Document, GAMS (module 680; package TOMS), MathReview, ZentralBlatt

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1st item.

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Algorithm 498: Airy functions using Chebyshev series approximations. ACM Trans. Math. Software 1 (4), pp. 372–379.

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ISSN 0098-3500, Document, GAMS (module 498; package TOMS), ZentralBlatt

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1st item, 4th item.

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23: Bibliography M

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Algorithm AS 245. A robust and reliable algorithm for the logarithm of the gamma function. Appl. Statist. 38 (2), pp. 397–402.

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FullText, Code, ZentralBlatt

Referenced by:

5th item.

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Algorithm AS 63. The incomplete beta integral. Appl. Statist. 22 (3), pp. 409–411.

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Notes:

Double-precision Fortran. For remark see same journal 26 (1977), pp. 111-114

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FullText, Code

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4th item.

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Algorithm 149: Complete elliptic integral. Comm. ACM 5 (12), pp. 605.

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Notes:

Includes Algol program, maximum accuracy 10D. For remark see ACM Trans. Math. Software 4 (1978), p. 95

External Links:

ISSN 0001-0782, Document

Referenced by:

§19.39(ii).

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Algorithm AS 187. Derivatives of the incomplete gamma integral. Appl. Statist. 31 (3), pp. 330–335.

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Notes:

Single-precision Fortran.

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FullText, Code, Document, ZentralBlatt

Referenced by:

4th item.

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Elementary Functions: Algorithms and Implementation. Birkhäuser Boston Inc., Boston, MA.

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Notes:

A 2nd edition was published in 2006.

External Links:

ISBN 0-8176-3990-X, MathReview (Warren E. Ferguson, Jr.), ZentralBlatt

Referenced by:

§4.45(i).

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24: Bibliography W

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Algorithm 794: Numerical Hankel transform by the Fortran program HANKEL. ACM Trans. Math. Software 25 (2), pp. 240–250.

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Notes:

Double-precision Fortran, maximum accuracy 10S.

External Links:

ISSN 0098-3500, Document, GAMS (module 794; package TOMS), ZentralBlatt

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7th item, 10th item.

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A rational approximant for the digamma function. Numer. Algorithms 33 (1-4), pp. 499–507.

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Notes:

International Conference on Numerical Algorithms, Vol. I (Marrakesh, 2001)

External Links:

ISSN 1017-1398, Document, MathReview, ZentralBlatt

Referenced by:

§3.9(vi), §5.23(i).

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Asymptotic Approximations to Truncation Errors of Series Representations for Special Functions. In Algorithms for Approximation, A. Iske and J. Levesley (Eds.), pp. 331–348.

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External Links:

ISBN 3-540-33283-9, Document, MathReview Entry, ZentralBlatt

Referenced by:

§2.10(i).

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An algorithmic proof theory for hypergeometric (ordinary and “$q$”) multisum/integral identities. Invent. Math. 108, pp. 575–633.

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External Links:

ISSN 0020-9910, Document, MathReview (David R. Masson), ZentralBlatt

Referenced by:

§16.4(iii).

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Algorithm 44: Bessel functions computed recursively. Comm. ACM 4 (4), pp. 177–178.

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Notes:

Includes Algol code, maximum accuracy 8S.

External Links:

ISSN 0001-0782, Document

Referenced by:

§10.77(ii).

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25: 9.17 Methods of Computation

… ►The second method is to apply generalized Gauss–Laguerre quadrature (§3.5(v)) to the integral (9.5.8). For the second method see also Gautschi (2002a). … ►In consequence of §9.6(i), algorithms for generating Bessel functions, Hankel functions, and modified Bessel functions (§10.74) can also be applied to $\mathrm{Ai}\left(z\right)$, $\mathrm{Bi}\left(z\right)$, and their derivatives. …

26: 17.19 Software

… ►In this section we provide links to the research literature describing the implementation of algorithms in software for the evaluation of functions described in this chapter. …

27: 26.22 Software

… ►In this section we provide links to the research literature describing the implementation of algorithms in software for the evaluation of functions described in this chapter. … ►

Stony Brook Algorithm Repository (website).

… ►For algorithms for counting and analyzing combinatorial structures see Knuth (1993), Nijenhuis and Wilf (1975), and Stanton and White (1986).

28: 27.18 Methods of Computation: Primes

… ►Two simple algorithms for proving primality require a knowledge of all or part of the factorization of $n-1,n+1$, or both; see Crandall and Pomerance (2005, §§4.1–4.2). These algorithms are used for testing primality of Mersenne numbers, $2^n-1$, and Fermat numbers, $2^{2^n}+1$. … ►The APR (Adleman–Pomerance–Rumely) algorithm for primality testing is based on Jacobi sums. … ►The AKS (Agrawal–Kayal–Saxena) algorithm is the first deterministic, polynomial-time, primality test. … ►The ECPP (Elliptic Curve Primality Proving) algorithm handles primes with over 20,000 digits. …

29: Bibliography B

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Algorithm 719: Multiprecision translation and execution of Fortran programs. ACM Trans. Math. Software 19 (3), pp. 288–319.

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External Links:

ISSN 0098-3500, Document, GAMS (module 719; package TOMS), C++ wrapper, ZentralBlatt

Referenced by:

3rd item, 2nd item.

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An algorithm for regular and irregular Coulomb and Bessel functions of real order to machine accuracy. Comput. Phys. Comm. 21 (3), pp. 297–314.

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External Links:

Document

Referenced by:

§3.10(iii), §33.22(iv).

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Bounds and algorithms for the $K$-Bessel function of imaginary order. LMS J. Comput. Math. 16, pp. 78–108.

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External Links:

ISSN 1461-1570, Document, MathReview (Jürgen Müller), ZentralBlatt

Referenced by:

§10.45, §10.45.

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Algorithm 21: Bessel function for a set of integer orders. Comm. ACM 3 (11), pp. 600.

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Notes:

Includes Algol code, minimum accuracy 5S. For certification see same journal 8(1965), p. 219.

External Links:

ISSN 0001-0782, Document

Referenced by:

§10.77(ii).

Encodings:

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Algorithm 524: MP, A Fortran multiple-precision arithmetic package [A1]. ACM Trans. Math. Software 4 (1), pp. 71–81.

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External Links:

ISSN 0098-3500, Document, Remark. GAMS (module 524; package TOMS)

Referenced by:

3rd item, 1st item, 1st item, 1st item, 3rd item, 1st item, 1st item.

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30: Bibliography D

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Computing Riemann theta functions. Math. Comp. 73 (247), pp. 1417–1442.

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Notes:

Two of the authors (Deconinck and van Hoeij) have developed Maple code for the algorithms described in this paper.

External Links:

ISSN 0025-5718, Document, Code, MathReview, ZentralBlatt

Referenced by:

§21.10(i), 1st item, §21.2(i), §21.4, M. Heil (1995).

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Algorithm 654: Fortran subroutines for computing the incomplete gamma function ratios and their inverses. ACM Trans. Math. Software 13 (3), pp. 318–319.

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Notes:

Single-precision Fortran, maximum accuracy 14D.

External Links:

ISSN 0098-3500, Document, GAMS (module 654; package TOMS), ZentralBlatt

Referenced by:

1st item.

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Algorithm 708: Significant digit computation of the incomplete beta function ratios. ACM Trans. Math. Software 18 (3), pp. 360–373.

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Notes:

Single-precision Fortran, maximum accuracy 14D.

External Links:

ISSN 0098-3500, Document, GAMS (module 708; package TOMS), ZentralBlatt

Referenced by:

3rd item.

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A simplified algorithm for the second-order sound fields. J. Acoust. Soc. Amer. 108 (6), pp. 2759–2764.

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External Links:

Document

Referenced by:

§8.24(iii).

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Algorithm 322. F-distribution. Comm. ACM 11 (2), pp. 116–117.

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Notes:

Includes Algol program, maximum accuracy 10S. For certification see same journal 12(1969), p. 39

External Links:

ISSN 0001-0782, Document

Referenced by:

§8.28(iv).

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