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- FEE_method abstract "In mathematics, the FEE method is the method of fast summation of series of a special form. It was constructed in 1990 by E. A. Karatsuba and was called FEE—Fast E-function Evaluation—because it makes it possible fast computations of the Siegel -functions, and in particular, A class of functions, which are 'similar to the exponential function' was given the name 'E-functions' by Siegel. Among these functions are such special functions as the hypergeometric function, cylinder, spherical functions and so on. Using the FEE, it is possible to prove the following theorem Theorem: Let be an elementary Transcendental function, that is the exponential function, or a trigonometric function, or an elementary algebraic function, or their superposition, or their inverse, or a superposition of the inverses. Then Here is the complexity of computation (bit) of the function with accuracy up to digits, is the complexity of multiplication of two -digit integers.The algorithms based on the method FEE include the algorithms for fast calculation of any elementary Transcendental function for any value of the argument, the classical constants e, the Euler constant the Catalan and the Apéry constants, such higher transcendental functions as the Euler gamma function and its derivatives, the hypergeometric, spherical, cylinder (including the Bessel) functions and some other functions foralgebraic values of the argument and parameters, the Riemann zeta function for integer values of the argument and the Hurwitz zeta function for integer argument and algebraic values of the parameter, and also such special integrals as the integral of probability, the Fresnel integrals, the integral exponential function, the trigonometric integrals, and some other integrals for algebraic values of the argument with the complexity bound which is close to the optimal one, namelyAt present, only the FEE makes it possible to calculate fast the values of the functions from the class of higher transcendental functions, certain special integrals of mathematical physics and such classical constants as Euler's, Catalan's and Apéry's constants. An additional advantage of the method FEE is the possibility of parallelizing the algorithms based on the FEE.".
- FEE_method wikiPageExternalLink algen.htm.
- FEE_method wikiPageExternalLink divcen.htm.
- FEE_method wikiPageID "21674054".
- FEE_method wikiPageRevisionID "545582781".
- FEE_method hasPhotoCollection FEE_method.
- FEE_method subject Category:Computer_arithmetic_algorithms.
- FEE_method subject Category:Numerical_analysis.
- FEE_method subject Category:Pi_algorithms.
- FEE_method type Abstraction100002137.
- FEE_method type Act100030358.
- FEE_method type Activity100407535.
- FEE_method type Algorithm105847438.
- FEE_method type ArbitraryPrecisionAlgorithms.
- FEE_method type Event100029378.
- FEE_method type PiAlgorithms.
- FEE_method type Procedure101023820.
- FEE_method type PsychologicalFeature100023100.
- FEE_method type Rule105846932.
- FEE_method type YagoPermanentlyLocatedEntity.
- FEE_method comment "In mathematics, the FEE method is the method of fast summation of series of a special form. It was constructed in 1990 by E. A. Karatsuba and was called FEE—Fast E-function Evaluation—because it makes it possible fast computations of the Siegel -functions, and in particular, A class of functions, which are 'similar to the exponential function' was given the name 'E-functions' by Siegel.".
- FEE_method label "FEE method".
- FEE_method label "Метод БВЕ".
- FEE_method sameAs m.05mv1zs.
- FEE_method sameAs Q4291816.
- FEE_method sameAs Q4291816.
- FEE_method sameAs FEE_method.
- FEE_method wasDerivedFrom FEE_method?oldid=545582781.
- FEE_method isPrimaryTopicOf FEE_method.