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  • 1
    Electronic Resource
    Electronic Resource
    On the convergence rates of subdivision algorithms for box spline surfaces (1985)
    Springer
    Constructive approximation 1 (1985), S. 305-322 
    Details
    ISSN: 1432-0940
    Keywords: 41A15 ; Box spline ; Convergence rate ; Subdivision algorithms ; Control net
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Dahmen and Micchelli [8] have shown that in general the coefficients of the refined control nets of a box spline surface converge to the surface at (at least) the rate of the refinement. The purpose of this article is to show that under mild additional assumptions the convergence rate is even quadratic. Although this rate is in general best possible, we point out under what circumstances even higher rates are obtained (locally).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01890038
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Algebraic properties of discrete box splines (1987)
    Springer
    Constructive approximation 3 (1987), S. 209-221 
    Details
    ISSN: 1432-0940
    Keywords: Discrete box splines ; Discrete truncated powers ; Linear independence ; Piecewise structure ; Number of solutions to linear diophantine equations ; 41A15 ; 41A63 ; 39A70 ; 10B30 ; 10A21 ; 10A50 ; 05B35
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The central objective of this paper is to discuss linear independence of translates of discrete box splines which we introduced earlier as a device for the fast computation of multivariate splines. The results obtained here allow us to draw conclusions about the structure of such discrete splines which have, in particular, applications to counting the number of nonnegative integer solutions of linear diophantine equations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01890565
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    Paper (German National Licenses)
    Fulltext
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