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  • Articles  (3)
  • Other Sources
  • AMS(MOS): 65D15  (3)
  • 1985-1989
  • 1980-1984  (3)
  • 1983  (3)
  • Mathematics  (3)
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  • Articles  (3)
  • Other Sources
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Years
  • 1985-1989
  • 1980-1984  (3)
Year
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  • Mathematics  (3)
  • 1
    Electronic Resource
    Electronic Resource
    A stable method for the evaluation of a polynomial and of a rational function of one variable (1983)
    Springer
    Numerische Mathematik 41 (1983), S. 309-319 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65D15 ; 65G05 ; CR: 5.11
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary It is shown that if one uses a carefully defined concept of stability (Stewart, G.W., Introduction to matrix computations, Academic Press, New York and London, 1973) then Horner's rule for the evaluation of a polynomial and some other evaluation methods are not always stable. A method is presented which is always stable. The operations count for this method is the same as that for Horner's rule. The method is generalized to apply to all rational functions of one variable.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01418328
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    A Remez type algorithm for spline functions (1983)
    Springer
    Numerische Mathematik 41 (1983), S. 117-146 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65D15 ; CR: 5.13
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary A Remez type algorithm for computing best spline approximations of degreen withk fixed knots is developed. It is shown that the sequence constructed in the algorithm converges to a best approximation, ifk≦n+1, and at least to a nearly best approximation, ifk〉n+1. In contrast to the standard interpolation methods no restriction to the position of the knots is required. This fact may be important to treat approximation problems for splines with free knots.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01396309
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  • 3
    Electronic Resource
    Electronic Resource
    The QD-algorithm and multivariate Padé-approximants (1983)
    Springer
    Numerische Mathematik 42 (1983), S. 259-269 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65D15 ; CR: 5.13
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary The quotient-difference (QD) algorithm can be used to construct univariate Padé-approximants [1]. In this paper we see that it can also be used to construct the multivariate Padé-approximants introduced in [3], just by reformulating the quotient-difference algorithm as in Sect. 1. The multivariate Padé-approximants and the multivariate QD-scheme are treated in the Sects. 2 and 3 respectively. Thus for this type of multivariate Padé-approximants a link with the theory of multivariate continued fractions is established.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01389572
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    Paper (German National Licenses)
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