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  • integration
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  • Articles  (4)
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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    BIT 10 (1970), S. 277-294 
    ISSN: 1572-9125
    Keywords: Numerical ; integration ; derivative ; extrapolation ; error term
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Some quadrature formulae using the derivatives of the integrand are discussed. As special cases are obtained generalizations of both the ordinary and the modified Romberg algorithms. In all cases the error terms are expressed in terms of Bernoulli polynomials and functions.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    BIT 7 (1967), S. 103-113 
    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
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Journal of intelligent and robotic systems 22 (1998), S. 129-141 
    ISSN: 1573-0409
    Keywords: integration ; sensor fusion ; map building ; localisation ; artificial vision ; reactive navigation ; mobile robotics ; autonomous systems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract A conventional autonomous mobile robot is introduced. The main idea is the integration of many conventional and sophisticated sensor fusion techniques, introduced by several authors in recent years. We show the actual possibility of integrating all these techniques together, rather than analyzing implementation details. The topics of multisensor fusion, observation integration and sensor coordination are widely used throuhout the article. The final goal is to demonstrate the validity of both mathematical and artificial intelligence techniques in guaranteeing vehicle survival in a dynamic environment, while the robot carries out a specific task. We review conventional techniques for the management of uncertainty while we describe an implementation of a mobile robot which combines on-line heterogeneous sensors in its navigation and localisation tasks.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Mathematical notes 64 (1998), S. 476-482 
    ISSN: 1573-8876
    Keywords: integration ; fractal curve ; integration over a rectifiable curve ; integration density ; jump problem ; Cauchy transform of a distribution ; continuous integration ; discontinuous integration
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A definition of integration, i.e., a generalization of a functional of the form $$u(z) \mapsto \smallint _\Gamma f(z)u(z) dz$$ to the case where Γ is a fractal curve on the complex plane andƒ(z) (integration density) is a function defined on this curve is given. The existence and uniqueness of the integral with given density are examined.
    Type of Medium: Electronic Resource
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