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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Numerische Mathematik 74 (1996), S. 177-201 
    ISSN: 0945-3245
    Keywords: Mathematics Subject Classification (1991): 65M60 41A15 41A29 41A63; 65N30 76M25
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary. Radial basis functions are used in the recovery step of finite volume methods for the numerical solution of conservation laws. Being conditionally positive definite such functions generate optimal recovery splines in the sense of Micchelli and Rivlin in associated native spaces. We analyse the solvability to the recovery problem of point functionals from cell average values with radial basis functions. Furthermore, we characterise the corresponding native function spaces and provide error estimates of the recovery scheme. Finally, we explicitly list the native spaces to a selection of radial basis functions, thin plate splines included, before we provide some numerical examples of our method.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Numerical algorithms 16 (1997), S. 155-170 
    ISSN: 1572-9265
    Keywords: scattered data approximation ; radial basis functions ; triangulation methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract A Detection Algorithm for the localisation of unknown fault lines of a surface from scattered data is given. The method is based on a local approximation scheme using thin plate splines, and we show that this yields approximation of second order accuracy instead of first order as in the global case. Furthermore, the Detection Algorithm works with triangulation methods, and we show their utility for the approximation of the fault lines. The output of our method provides polygonal curves which can be used for the purpose of constrained surface approximation.
    Type of Medium: Electronic Resource
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  • 3
    Book
    Book
    Berlin :Springer,
    Title: Multiresolution methods in scattered data modelling /; 37
    Author: Iske, Armin
    Edition: 1. Aufl.
    Publisher: Berlin :Springer,
    Year of publication: 2004
    Pages: XII, 182 S.
    Series Statement: Lecture notes in computational science and engineering 37
    ISBN: 3-540-20479-2
    Type of Medium: Book
    Language: German
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