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  • Articles  (5)
  • 65H10  (5)
  • Springer  (5)
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  • Articles  (5)
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  • Springer  (5)
  • American Meteorological Society
  • American Physical Society (APS)
  • Blackwell Publishing Ltd
  • Cambridge University Press
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  • 2000-2004
  • 1995-1999
  • 1980-1984  (5)
  • 1955-1959
  • 1935-1939
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  • Computer Science  (5)
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  • Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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  • 1
    Electronic Resource
    Electronic Resource
    On the R-order of coupled sequences III (1983)
    Springer
    Computing 30 (1983), S. 157-169 
    Details
    ISSN: 1436-5057
    Keywords: 65H10 ; 15A48 ; Iterative parallel processes ; best individualR-orders ; ordered positive decomposition
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Für konvergente Folgen {x n,1 },...,{x n,s }, welche über ein System (2) von Ungleichungen miteinander verkoppelt sind, werden die besten individuellenR-Ordnungen τ1,...,τ s bestimmt. Dazu wird gezeigt, daß diese gleich den Spektralradien von bestimmten Matrizen sind, welche aus Exponenten in (2) gebildet werden.
    Notes: Abstract For convergent sequences {x n,1 },...{x n,s } coupled by a system (2) of inequalities the optimal individualR-orders τ1,...,τ s are determined as the spectral radii of certain matrices composed of exponents appearing in (2).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02280786
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Secant methods for sparse systems of nonlinear equations with a special structure (1983)
    Springer
    Computing 30 (1983), S. 213-223 
    Details
    ISSN: 1436-5057
    Keywords: 65H10 ; 65L10 ; Sparse systems of nonlinear equations ; secant methods ; boundary value problems ; multiple shooting method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Es werden Sekantenverfahren für solche schwach besetzten nichtlinearen Gleichungssysteme mit spezieller Struktur angegeben, wie sie zum Beispiel bei der Lösung von Randwertaufgaben für Systeme von gewöhnlichen Differentialgleichungen mit der Mehrzielmethode entstehen. Die angegebenen Verfahren werden mit einem angepaßten Broyden-Verfahren verglichen.
    Notes: Abstract Secant methods for sparse systems of nonlinear equations with a special structure are given, as they arise, e. g., in the solution of boundary value problems for systems of ordinary differential equations by multiple shooting. The presented methods are compared with an adapted Broyden method.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02253894
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  • 3
    Electronic Resource
    Electronic Resource
    Zur Charakterisierung und Berechnung von symmetrischen Kubaturformeln (1983)
    Springer
    Computing 31 (1983), S. 211-230 
    Details
    ISSN: 1436-5057
    Keywords: 65D32 ; 41A55 ; 41A63 ; 65H10 ; 68A15 ; Cubature formulas ; systems of non-linear equations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Abstract The paper is concerned with the characterization and calculation of symmetric cubature formulae of degree 2k−1 for two-dimensional product-functionals. The number of knots of the cubature formulae satisfies the following relation: $$\frac{{k(k + 1)}}{2} + \left[ {\frac{k}{2}} \right] \leqslant r \leqslant \frac{{k(k + 1)}}{2} + \left[ {\frac{k}{2}} \right] + 1.$$ The systems of non-linear equations involved are either solved exactly or all solutions are computed with any precision using a program-package for symbolic and algebraic calculations.
    Notes: Zusammenfassung Diese Arbeit befaßt sich mit der Charakterisierung und Berechnung von symmetrischen Kubaturformeln vom Grad 2k−1 für zweidimensionale Produktfunktionale. Die Knotenanzahlr der Kubaturformeln genügt der folgenden Ungleichung: $$\frac{{k(k + 1)}}{2} + \left[ {\frac{k}{2}} \right] \leqslant r \leqslant \frac{{k(k + 1)}}{2} + \left[ {\frac{k}{2}} \right] + 1.$$ Die dabei auftretenden nichtlinearen Gleichungssysteme werden entweder exakt gelöst oder alle Lösungen werden mit beliebiger Genauigkeit mit Hilfe eines Programmpaketes für symbolische und algebraische Berechnungen ermittelt.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02263432
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  • 4
    Electronic Resource
    Electronic Resource
    A remark about the convergence of interval sequences (1983)
    Springer
    Computing 31 (1983), S. 255-259 
    Details
    ISSN: 1436-5057
    Keywords: 65G10 ; 65H10 ; 65J15 ; Systems of equations ; interval operators ; interval iterations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Bei manchen Intervalliterationen wird zur Konvergenz einer entsprechenden Intervallfolge vorausgesetzt, daß σ(r)〈1 ist, wobei σ den Spektralradius vonr bezeichnet undr eine nichtnegative Lipschitzmatrix ist. In dieser Arbeit werden die Aussagen auf den Fall σ(r)=1 erweitert.
    Notes: Abstract By some interval iterations the condition σ(r)〈1 will be assumed for the convergence of the corresponding interval sequence by which σ denotes the spectral radius ofr, andr is a nonnegative Lipschitz matrix. In this paper the theorems are extended for the case σ (r)=1.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02263435
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  • 5
    Electronic Resource
    Electronic Resource
    Interval operators of a function of which the Lipschitz matrix is an interval M-matrix (1983)
    Springer
    Computing 31 (1983), S. 245-253 
    Details
    ISSN: 1436-5057
    Keywords: 65G10 ; 65H10 ; 65J15 ; Systems of equations ; interval operators ; interval iterations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Es gibt verschiedene Intervalliterationen unter Verwendung von Intervalloperatoren, welche eine Folge von Intervallen zur Einschließung aller Lösungen einer Gleichungf(x)=0 in einem gegebenen IntervallX 0 liefern und welche die Kenntnis einer Lipschitz-IntervallmatrixL vonf erfordern. In dieser Arbeit werden Existenz-und Konvergenzaussagen für den Fall gemacht, daßL eineM-Intervallmatrix ist.
    Notes: Abstract There are several interval iterations by applying interval operators which supply an interval sequence including all solutions of an equationf(x)=0 in a given intervalX 0 and which require the knowledge of an interval Lipschitz matrixL off. In this paper statements are made about existence and convergence in case thatL is an intervalM-matrix.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02263434
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