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  • Articles  (33)
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  • 41A15  (33)
  • 1985-1989  (33)
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  • Mathematics  (33)
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  • Articles  (33)
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  • 1
    Electronic Resource
    Electronic Resource
    Convex interpolating splines of arbitrary degree. III (1986)
    Springer
    BIT 26 (1986), S. 527-536 
    Details
    ISSN: 1572-9125
    Keywords: 41A15
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract For given data (x i, fi) i=0 n (x 0〈x 1〈...〈x n) we consider the possibility of finding a spline functions of arbitrary degreek (k≧3) with preassigned smoothnessl, where 1≦l≦[(k-1)/2]. The splines should be such thats(x i)=f i (i=0, 1,...,n) ands is convex or nondecreasing and convex on [x 0,x n]. An explicit formula for this function as well as the conditions that guarantee the required properties are established. An algorithm for the determination of the splines and the error bounds is also included.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01935058
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  • 2
    Electronic Resource
    Electronic Resource
    A recursion relation for simple rationalB-splines (1987)
    Springer
    BIT 27 (1987), S. 282-284 
    Details
    ISSN: 1572-9125
    Keywords: 65D07 ; 41A15
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01934190
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  • 3
    Electronic Resource
    Electronic Resource
    A shape preserving area true approximation of histogram by rational splines (1988)
    Springer
    BIT 28 (1988), S. 329-339 
    Details
    ISSN: 1572-9125
    Keywords: 65D07 ; 41A15
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract For a given histogram, we consider an application of a simple rational spline to a shape preserving area true approximation of the histogram. An algorithm for determination of the spline is as easy as one with a quadratic polynomial spline, while the latter does not always preserve the shape of the histogram. Some numerical examples are given at the end of the paper.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01934096
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  • 4
    Electronic Resource
    Electronic Resource
    Positivity of cubic polynomials on intervals and positive spline interpolation (1988)
    Springer
    BIT 28 (1988), S. 340-352 
    Details
    ISSN: 1572-9125
    Keywords: 65D17 ; 41A15 ; 90C20 ; Positivity of cubic polynomials ; nonnegative spline interpolants minimal curvature ; dual program ; return-formula
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A criterion for the positivity of a cubic polynomial on a given interval is derived. By means of this result a necessary and sufficient condition is given under which cubicC 1-spline interpolants are nonnegative. Further, since such interpolants are not uniquely determined, for selecting one of them the geometric curvature is minimized. The arising optimization problem is solved numerically via dualization.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01934097
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  • 5
    Electronic Resource
    Electronic Resource
    Positive interpolation with rational splines (1989)
    Springer
    BIT 29 (1989), S. 140-147 
    Details
    ISSN: 1572-9125
    Keywords: AMS(MOS) 65D07 ; 41A15
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A method is presented for the construction of positive rational splines of continuity classC 2.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01932711
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  • 6
    Electronic Resource
    Electronic Resource
    Short proof of an identity of Gaffney (1989)
    Springer
    BIT 29 (1989), S. 155-156 
    Details
    ISSN: 1572-9125
    Keywords: 41A15 ; 65D07 ; B-splines ; Gaffney's identity ; recurrence relations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01932713
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  • 7
    Electronic Resource
    Electronic Resource
    Fully discrete approximation methods for the estimation of parabolic systems and boundary parameters (1986)
    Springer
    Acta applicandae mathematicae 7 (1986), S. 1-34 
    Details
    ISSN: 1572-9036
    Keywords: 41A15 ; 65N30 ; Parabolic systems ; parameter estimation ; approximation methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A spatially and temporally discrete numerical approximation scheme is developed for the identification of a class of semilinear parabolic systems with unknown boundary parameters. The identification problem is formulated as a least squares fit to data subject to an equivalent representation for the dynamics in the form of an abstract evolution equation. Finite-dimensional difference equation state approximations are constructed using a cubic spline-based, Galerkin method and the Padé rational function approximations to the exponential. A sequence of approximating identification problems result, the solutions of which are shown to exist and, in a certain sense, approximate solutions to the original identification problem. Numerical results for two examples, one involving the modeling of biological mixing in deep sea sediment cores, and the other, the estimation of transport parameters for indoor mixing, are discussed. In both examples, the identification is based upon actual experimental data.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00046975
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  • 8
    Electronic Resource
    Electronic Resource
    Reflections on value regions, limit regions and truncation errors for continued fractions (1985)
    Springer
    Numerische Mathematik 47 (1985), S. 191-215 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 30B70 ; 40A15 ; 41A15 ; CR: G1.2
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary For continued fractionsK(a n /1) the concept of limit region is discussed, and its use for obtaining modified truncation error estimates is illustrated on examples. A certain strategy for numerical computation of limit regions is presented and illustrated on examples.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01389709
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  • 9
    Electronic Resource
    Electronic Resource
    Lösung von Differentialgleichungen mit Splinefunktionen. Eine Störungstheorie (1986)
    Springer
    Numerische Mathematik 48 (1986), S. 323-336 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65L05 ; 65L07 ; 65D07 ; 65D10 ; 41A15 ; CR: G.1.7 ; G.1.2
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary In this paper non-linear splines (depending onn+1 parameters) are used to patch up the solution of an initial value problem in intervals of stepsizeh. The elements of the solution are fixed byq smoothness conditions andd conditions derived from the differential equation in an appropriate setup. The feasibility of the method can be connected to that of the polynomial spline method by a perturbation type argument. Thus the question of convergence forh→0 is closely connected to the linear (polynomial) case. A new elementary prove is given for divergence of the polynomial splines ifq is larger thand+1, as was done by Mülthei [4] with other techniques. A byproduct is an extention of the famous result for polynomial interpolation by Runge on equidistant grids that interpolation of a given function by splines of too high smoothness can cause divergence forh→0.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01389478
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  • 10
    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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