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  • AMS (MOS)  (1)
  • barycentric representation  (1)
  • 1
    Electronic Resource
    Electronic Resource
    Baryzentrische Formeln zur Trigonometrischen Interpolation (I) (1984)
    Springer
    Zeitschrift für angewandte Mathematik und Physik 35 (1984), S. 91-105 
    Details
    ISSN: 1420-9039
    Keywords: AMS (MOS) ; 65D05 ; 65T05
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Description / Table of Contents: Résumé Des formules barycentriques pour l'interpolation d'une fonction périodiquef par un polynôme trigonométrique ont été données par Salzer [11] pour le cas d'un nombre impair de noeuds quelconques et par Henrici [7] dans le cas particulier de noeuds équidistants. Nous présentons ici des formules pour l'interpolation avec un nombre pair de noeuds quelconques, ainsi que des versions simplifiées pour une fonctionf paire ou impaire.
    Notes: Summary Barycentric formulas for the interpolation of a periodic functionf by a trigonometric polynomial have been given by Salzer [11] in the case of an odd number of arbitrary (interpolating) points and by Henrici [7] in the special case of equidistant points. We present here formulas for the interpolation with an even number of arbitrary points as well as simpler versions for an even or an odd functionf.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00945179
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    A matrix for determining lower complexity barycentric representations of rational interpolants (2000)
    Springer
    Numerical algorithms 24 (2000), S. 17-29 
    Details
    ISSN: 1572-9265
    Keywords: interpolation ; rational interpolation ; barycentric representation ; barycentric weights ; complexity ; 65D05 ; 41A05 ; 41A20
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Among the representations of rational interpolants, the barycentric form has several advantages, for example, with respect to stability of interpolation, location of unattainable points and poles, and differentiation. But it also has some drawbacks, in particular the more costly evaluation than the canonical representation. In the present work we address this difficulty by diminishing the number of interpolation nodes embedded in the barycentric form. This leads to a structured matrix, made of two (modified) Vandermonde and one Löwner, whose kernel is the set of weights of the interpolant (if the latter exists). We accordingly modify the algorithm presented in former work for computing the barycentric weights and discuss its efficiency with several examples.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1019180807534
    Library Location Call Number Volume/Issue/Year Availability
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    Paper (German National Licenses)
    Fulltext
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