relative precision
(0.001 seconds)
1—10 of 14 matching pages
1: 7.24 Approximations
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Cody (1969) provides minimax rational approximations for and . The maximum relative precision is about 20S.
Cody et al. (1970) gives minimax rational approximations to Dawson’s integral (maximum relative precision 20S–22S).
2: 3.1 Arithmetics and Error Measures
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►Symmetric rounding or rounding to nearest of gives or , whichever is nearer to , with maximum relative error equal to the machine precision
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►Also in this arithmetic generalized precision can be defined, which includes absolute error and relative precision (§3.1(v)) as special cases.
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►The relative precision is
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3.1.10
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3: 19.15 Advantages of Symmetry
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►Symmetry allows the expansion (19.19.7) in a series of elementary symmetric functions that gives high precision with relatively few terms and provides the most efficient method of computing the incomplete integral of the third kind (§19.36(i)).
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4: 3.10 Continued Fractions
5: 27.17 Other Applications
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►Schroeder (2006) describes many of these applications, including the design of concert hall ceilings to scatter sound into broad lateral patterns for improved acoustic quality, precise measurements of delays of radar echoes from Venus and Mercury to confirm one of the relativistic effects predicted by Einstein’s theory of general relativity, and the use of primes in creating artistic graphical designs.
6: 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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Algorithm 985: Simple, Efficient, and Relatively Accurate Approximation for the Evaluation of the Faddeyeva Function.
ACM Trans. Math. Softw. 44 (2), pp. 22:1–22:9.
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Computation of Special Functions.
John Wiley & Sons Inc., New York.
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7: DLMF Project News
error generating summary8: 25.20 Approximations
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Cody et al. (1971) gives rational approximations for in the form of quotients of polynomials or quotients of Chebyshev series. The ranges covered are , , , . Precision is varied, with a maximum of 20S.
9: Bibliography G
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On high precision methods for computing integrals involving Bessel functions.
Math. Comp. 33 (147), pp. 1049–1057.
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Algorithm 222: Incomplete beta function ratios.
Comm. ACM 7 (3), pp. 143–144.
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Algorithm 542: Incomplete gamma functions.
ACM Trans. Math. Software 5 (4), pp. 482–489.
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Variable-precision recurrence coefficients for nonstandard orthogonal polynomials.
Numer. Algorithms 52 (3), pp. 409–418.
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Dirichlet convolution of cotangent numbers and relative class number formulas.
Monatsh. Math. 110 (3-4), pp. 231–256.
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10: Bibliography S
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General relativity and quantum mechanics: towards a generalization of the Lambert function: a generalization of the Lambert function.
Appl. Algebra Engrg. Comm. Comput. 17 (1), pp. 41–47.
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Efficient multiple-precision evaluation of elementary functions.
Math. Comp. 52 (185), pp. 131–134.
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Algorithm 693: A FORTRAN package for floating-point multiple-precision arithmetic.
ACM Trans. Math. Software 17 (2), pp. 273–283.
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On the relative extrema of ultraspherical polynomials.
Boll. Un. Mat. Ital. (3) 5, pp. 125–127.
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On the relative extrema of the Hermite orthogonal functions.
J. Indian Math. Soc. (N.S.) 15, pp. 129–134.
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