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  • 1
    Electronic Resource
    Electronic Resource
    Existence of Gaussian quadrature formulas for Birkhoff type data (1989)
    Springer
    Archiv der Mathematik 52 (1989), S. 588-594 
    Details
    ISSN: 1420-8938
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01237572
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Piecewise polynomial spaces and geometric continuity of curves (1989)
    Springer
    Numerische Mathematik 54 (1989), S. 319-337 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65D07 ; CR: G 1.2
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We say that a curve has geometric continuity if its curvatures and Frenet frame are continuous. In this paper we introduce spaces of piecewise polynomials which can be used to model space curves which have geometric continuity. We show that the basic theoretical properties of ordinary spline functions also hold for these spaces. These results extend and unify recent work on Beta-splines and Nu-splines which are used as a design tool in computer-aided geometric design of free form curves and surfaces.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01396765
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Generalized monosplines and optimal approximation (1985)
    Springer
    Constructive approximation 1 (1985), S. 137-154 
    Details
    ISSN: 1432-0940
    Keywords: 41A15 ; 41A5 ; 41A65 ; Perfect splines ; Monosplines ; Extended totally positive kernels ; Monotone norms ; Optimal quadrature formulas ; Optimal interpolation ; N-widths ; Optimal spaces
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Generalized monosplines of least norm are shown to exist and to determine optimal approximation processes such as numerical integration, interpolation and best approximating spaces. This extends various classical results related to monosplines and perfect splines, which are particular cases of generalized monosplines. The analysis here also provides for a unified treatment of the two classical classes of monosplines and perfect splines of least norm, and of their extremal properties.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01890027
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    Paper (German National Licenses)
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  • 4
    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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