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  • Articles  (2)
  • extrapolation  (2)
  • 1965-1969  (2)
  • Mathematics  (2)
  • Energy, Environment Protection, Nuclear Power Engineering
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  • Articles  (2)
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  • Mathematics  (2)
  • Energy, Environment Protection, Nuclear Power Engineering
  • 1
    Electronic Resource
    Electronic Resource
    Derivation of explicit expressions for the error terms in the ordinary and the modified Romberg algorithms (1969)
    Springer
    BIT 9 (1969), S. 18-29 
    Details
    ISSN: 1572-9125
    Keywords: Numerical ; integration ; extrapolation ; error term
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract It is proved that the error terms for both the ordinary and the modified Romberg algorithms may be expressed in terms of Bernoulli polynomials and their related periodic functions. The properties of the error terms may thus be described using the known properties of the Bernoulli polynomials and functions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01933536
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    On the practical application of the modified romberg algorithm (1967)
    Springer
    BIT 7 (1967), S. 103-113 
    Details
    ISSN: 1572-9125
    Keywords: Numerical ; integration ; extrapolation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Experience gained in the use of the modified Romberg algorithm is reported. An alternative form of the algorithm based on a cosine transformation of Euler-MacLaurin's and Euler's second formula is discussed. Some examples where the error estimate incorporated in the algorithm partly fails are given. Finally an ALGOL procedure combining the algorithm discussed in a previous paper of the author [1] and the modification discussed in this paper is described.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01934273
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    Paper (German National Licenses)
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