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  • Articles  (8)
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  • Articles  (8)
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  • Springer  (8)
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  • Oxford University Press
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  • 1980-1984  (8)
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  • Mathematics  (8)
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  • 1
    Electronic Resource
    Electronic Resource
    Approximants de pade-hermite. 1ère partie: theorie (1984)
    Springer
    Numerische Mathematik 43 (1984), S. 23-39 
    Details
    ISSN: 0945-3245
    Keywords: 65 B05 ; 65B10 ; 65E05 ; 30B70 ; CR: 5.13
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We present in this first paper a generalization of Padé approximants which gives us as particular cases Shafer's and Baker'sD-log approximants. First we define these approximants following an old idea of Hermite, then we prove some fundamental properties for their constructions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01389636
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  • 2
    Electronic Resource
    Electronic Resource
    On constrained multivariate splines and their approximations (1984)
    Springer
    Numerische Mathematik 43 (1984), S. 141-152 
    Details
    ISSN: 0945-3245
    Keywords: AMS (1980) Primary ; 41A29 ; Secondary, 65N15 ; 41A63 ; CR: 5.13
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary The variational formulation of multivariate spline functions is generalized to include cases where the function has to satisfy inequality constraints such as positivity and convexity. Condition for existence and uniqueness of a solution is given. Approximation to the solution can be obtained by solving the variational problem in a finite dimensional subspace. Conditions for convergence and error estimates of the approximations are presented, both for interpolation problems and smoothing problems. The general theory is illustrated by specific examples including the “volume-matching” problem and the “one-sided thin plate spline”.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01389643
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  • 3
    Electronic Resource
    Electronic Resource
    Padé-type approximants of exp (−z) whose denominators are (1+z/n) n (1984)
    Springer
    Numerische Mathematik 43 (1984), S. 283-292 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65D15 ; CR: 5.13
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary In this paper, we show that the sequences of Padé-type approximants (k−1/k) and (k/k) converge to exp (−z), uniformly and geometrically on every compact subset of the plane. A numerical study has been done, which discriminates these sequences from the point of view ofA-acceptability.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01390128
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  • 4
    Electronic Resource
    Electronic Resource
    Best constants occuring with the modulus of continuity in the error estimate for spline interpolants of odd degree on equidistant grids (1984)
    Springer
    Numerische Mathematik 44 (1984), S. 407-415 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65D15 ; CR: 5.13
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We deal with spline interpolants of odd degree on equidistant grids. The main interest is directed on cardinal and onn-periodic interpolation, wheren is odd. By the aid of an explicit representation of the interpolant by Euler-Frobenius-polynomials, we calculate the minimal constant occuring in the error estimate with the modulus of continuity.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01405571
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  • 5
    Electronic Resource
    Electronic Resource
    Approximants de Padé-Hermite 2ème partie: programmation (1984)
    Springer
    Numerische Mathematik 43 (1984), S. 41-57 
    Details
    ISSN: 0945-3245
    Keywords: 65B05 ; 65B10 ; 65E05 ; 30B70 ; CR: 5.13
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary In this second paper we propose an algorithm for the construction of the Δ-tables and of the Padé-Hermite tables [3]. Then we present some numerical applications.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01389637
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  • 6
    Electronic Resource
    Electronic Resource
    General order Newton-Padé approximants for multivariate functions (1984)
    Springer
    Numerische Mathematik 43 (1984), S. 293-307 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65D15 ; CR: 5.13
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Padé approximants are a frequently used tool for the solution of mathematical problems. One of the main drawbacks of their use for multivariate functions is the calculation of the derivatives off(x 1, ...,x p ). Therefore multivariate Newton-Padé approximants are introduced; their computation will only use the value off at some points. In Sect. 1 we shall repeat the univariate Newton-Padé approximation problem which is a rational Hermite interpolation problem. In Sect. 2 we sketch some problems that can arise when dealing with multivariate interpolation. In Sect. 3 we define multivariate divided differences and prove some lemmas that will be useful tools for the introduction of multivariate Newton-Padé approximants in Sect. 4. A numerical example is given in Sect. 5, together with the proof that forp=1 the classical Newton-Padé approximants for a univariate function are obtained.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01390129
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  • 7
    Electronic Resource
    Electronic Resource
    Error estimates for spline interpolants on equidistant grids (1984)
    Springer
    Numerische Mathematik 44 (1984), S. 417-424 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65D15 ; CR: 5.13
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary For oddm, the error of them-th-degree spline interpolant of power growth on an equidistant grid is estimated. The method is based on a decomposition formula for the spline function, which locally can be represented as an interpolation polynomial of degreem which is corrected by an (m+1)-st.-order difference term.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01405572
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  • 8
    Electronic Resource
    Electronic Resource
    Die Struktur der normalen rationalen Funktionen (1984)
    Springer
    Numerische Mathematik 43 (1984), S. 379-388 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65D15 ; 41A20 ; CR: 5.13
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We determine the connected components of the set of normal elements of the family ℛ m n [a,b] of rational functions. Numerical difficulties occuring with the computation of the Chebyshev approximation via the Remez algorithm can be caused by its disconnectedness. In order to illustrate this we give numerical examples.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01390180
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