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  • 1
    Electronic Resource
    Electronic Resource
    Order of approximation by electrostatic fields due to electrons (1985)
    Springer
    Constructive approximation 1 (1985), S. 121-135 
    Details
    ISSN: 1432-0940
    Keywords: 41 A 20 ; 30 E 10 ; Order of approximation ; Rational functions and electrostatic fields due to distribution of electrons ; Bers space ; Jordan domain ; Conformal mapping
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract LetD be a Jordan domain in the complex plane andA q (D) the Bers space with norm ∥ ∥ q . IfD is the unit disk, it is known that ∥S n 0∥2≥π/18, whereS n =∑ k=1 n l/(z−z nk ) withz nk ∈∂D, so that approximation in ∥ ∥ q ,q〈-2, is not possible. In this paper, we give an order of estimate of ∥f−S n ∥ q for 2〈q〈∞ when ∂D is a sufficiently smooth Jordan curve, and prove that this order of approximation is in general best possible.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01890026
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    On bivariate super vertex splines (1990)
    Springer
    Constructive approximation 6 (1990), S. 399-419 
    Details
    ISSN: 1432-0940
    Keywords: Multivariate ; Splines ; Super splines ; Approximation order ; Bézier net ; Interpolation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A vertex spline basis of the super-spline subspace $$\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{S} _d^r : = S_d^{r,r + \left\lfloor {(d - 2r - 1)/2} \right\rfloor } (\Delta )$$ of Sd r(Δ), where d≥3r+2 and Δ is an arbitrary triangulation inR 2, is constructed, so that the full approximation order ofd+1 can be achieved via an approximation formula using this basis.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01888272
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    Paper (German National Licenses)
    Fulltext
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