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  • Articles  (13)
  • CR: 5.13  (13)
  • 1995-1999
  • 1980-1984  (13)
  • 1925-1929
  • 1984  (8)
  • 1980  (5)
  • Mathematics  (13)
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  • Articles  (13)
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  • 1995-1999
  • 1980-1984  (13)
  • 1925-1929
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  • Mathematics  (13)
  • 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
    An alternative computational method for the approximation of random functions (1980)
    Springer
    Numerische Mathematik 35 (1980), S. 361-368 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS) 65D15 ; CR: 5.13
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary This paper shows that a computational procedure for approximation of random functions can be accomplished using purely linear programming techniques. This contrasts with previous results which use a twostage approach for the computation, one of which requires linear programming techniques. Computational results are given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01399005
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  • 5
    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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  • 6
    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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  • 7
    Electronic Resource
    Electronic Resource
    Strong uniqueness and second order convergence in nonlinear discrete approximation (1980)
    Springer
    Numerische Mathematik 34 (1980), S. 439-455 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65D15 ; CR: 5.13
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Strong uniqueness has proved to be an important condition in demonstrating the second order convergence of the generalised Gauss-Newton method for discrete nonlinear approximation problems [4]. Here we compare strong uniqueness with the multiplier condition which has also been used for this purpose. We describe strong uniqueness in terms of the local geometry of the unit ball and properties of the problem functions at the minimum point. When the norm is polyhedral we are able to give necessary and sufficient conditions for the second order convergence of the generalised Gauss-Newton algorithm.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01403680
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  • 8
    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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  • 9
    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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  • 10
    Electronic Resource
    Electronic Resource
    Reliable rational interpolation (1980)
    Springer
    Numerische Mathematik 36 (1980), S. 111-128 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65D05 ; CR: 5.13
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary A modification of the Thacher-Tukey algorithm for rational interpolation is proposed. The method employed demonstrates the reliability of the proposed algorithm as well as the reliability of the Thacher-Tukey algorithm. Furthermore, the proposed algorithm eliminates almost all the array storage space required to implement the Thacher-Tukey algorithm.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01396754
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  • 11
    Electronic Resource
    Electronic Resource
    Procedures for kernel approximation and solution of fredholm integral equations of the second kind (1980)
    Springer
    Numerische Mathematik 34 (1980), S. 125-141 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 41A15 ; 65R05 ; 68A10 ; CR: 5.13 ; 5.18
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary The purpose of this paper is to present explicit ALGOL procedures for (1) the approximation of a kernel (surface) by tensor products of splines, and (2) the computation of approximate eigenvalues and eigenfunctions for Fredholm integral equations of the second kind.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01396055
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  • 12
    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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  • 13
    Electronic Resource
    Electronic Resource
    Ein verallgemeinerter Kettenbruch-Algorithmus zur rationalen Hermite-Interpolation (1980)
    Springer
    Numerische Mathematik 36 (1980), S. 99-107 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65D05 ; CR: 5.13
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary In this paper we consider rational interpolation for an Hermite Problem, i.e. prescribed values of functionf and its derivatives. The algorithm presented here computes a solutionp/q of the linearized equationsp−fq=0 in form of a generalized continued fraction. Numeratorp and denominatorq of the solution attain minimal degree compatible with the linearized problem. The main advantage of this algorithm lies in the fact that accidental zeros of denominator calculated during the algorithm cannot lead to an unexpected stop of the algorithm. Unattainable points are characterized.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01395991
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