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  • 1
    Electronic Resource
    Electronic Resource
    On the uniqueness of generalized monosplines of least Lp-norm (1986)
    Springer
    Constructive approximation 2 (1986), S. 79-99 
    Details
    ISSN: 1432-0940
    Keywords: 41A15 ; 41A52 ; 41A55 ; Monosplines ; Perfect splines ; L p-Approximation ; Uniqueness of best approximation ; Degree theory
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The uniqueness of monosplines and perfect splines of leastL p-norm is treated in the framework of generalized monosplines and total positivity. The analysis is based on the invariance properties of the degree of a certain mapping and on a new composition result for totally positive kernels. For theL p-case 1〈p〈∞, uniqueness is shown under the same extra conditions as were previously shown to be needed in theL p-case. The uniqueness in theL ∞-case is obtained without any restrictions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01893418
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    On quasi-interpolation by radial basis functions with scattered centres (1995)
    Springer
    Constructive approximation 11 (1995), S. 239-254 
    Details
    ISSN: 1432-0940
    Keywords: Primary 41A15 ; 41A63 ; 41A25 ; 65D15 ; Secondary 41A30 ; 65D07 ; 65D10 ; Radial basis functions ; Quasi-interpolation ; Multivariate approximation ; Scattered data
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Approximation by radial basis functions with “quasi-uniformly” distributed centres inR d is discussed. A construction of new polynomially decaying functions that span the approximation space is presented and the properties of the quasi-interpolation operator with these functions are investigated. It is shown that the quasi-interpolant reproduces polynomials and gives approximation orders identical to those in the uniform square-grid case.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01203417
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    Paper (German National Licenses)
    Fulltext
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