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  • 2000-2004  (1)
  • 1980-1984  (1)
  • 1915-1919
  • Engineering General  (1)
  • Lagrange interpolation polynomial  (1)
  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Annals of the Institute of Statistical Mathematics 52 (2000), S. 557-573 
    ISSN: 1572-9052
    Keywords: Chebyshev polynomials ; convex combination ; extremal problems for polynomials ; Lagrange interpolation polynomial ; optimal discrimination designs
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The extrapolation design problem for polynomial regression model on the design space [−1,1] is considered when the degree of the underlying polynomial model is with uncertainty. We investigate compound optimal extrapolation designs with two specific polynomial models, that is those with degrees |m, 2m}. We prove that to extrapolate at a point z, |z| 〉 1, the optimal convex combination of the two optimal extrapolation designs |ξ m * (z), ξ2m * (z)} for each model separately is a compound optimal extrapolation design to extrapolate at z. The results are applied to find the compound optimal discriminating designs for the two polynomial models with degree |m, 2m}, i.e., discriminating models by estimating the highest coefficient in each model. Finally, the relations between the compound optimal extrapolation design problem and certain nonlinear extremal problems for polynomials are worked out. It is shown that the solution of the compound optimal extrapolation design problem can be obtained by maximizing a (weighted) sum of two squared polynomials with degree m and 2m evaluated at the point z, |z| 〉 1, subject to the restriction that the sup-norm of the sum of squared polynomials is bounded.
    Type of Medium: Electronic Resource
    Library Location Call Number Volume/Issue/Year Availability
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  • 2
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 1823-1840 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The optimality conditions for the optimal shape remodelling of linearly elastic plates are obtained by introducing the total variation of a function defined on a variable domain, although the variation of a function has been taken on a fixed domain in most literature on calculus of variations. Using these optimality conditions, a solution scheme involving an iterative algorithm is proposed, together with several numerical examples.
    Additional Material: 12 Ill.
    Type of Medium: Electronic Resource
    Library Location Call Number Volume/Issue/Year Availability
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