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  • 65H10  (3)
  • Newton's method  (2)
  • 2.4-diamino-6.7-dialkylpteridine  (1)
  • 65F15  (1)
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  • 1
    Electronic Resource
    Electronic Resource
    Safe bounds for the solutions of nonlinear problems using a parallel multisplitting method (1989)
    Springer
    Computing 42 (1989), S. 171-186 
    Details
    ISSN: 1436-5057
    Keywords: 65G10 ; 65H10 ; 65W05 ; CR: G. 1.0 ; G.1.5 ; Parallel methods ; nonlinear systems ; enclosures ; error bounds ; interval iterative methods ; multisplittings
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Für gewisse Systeme nichtlinearer GleichungenF(x)=0 entwicklen wir ein Verfahren, welches iterativ enge untere und obere Schranken für die Nullstellen vonF berechnet. Das Verfahren beruht auf einem Multisplitting für bestimmte Matrizen und weist so in natürlcher Weise Parallelität auf. Wir geben Kriterien für die Konvergenz der Schranken gegen die Nullstellen an und untersuchen die Konvergenzgeschwindigkeit.
    Notes: Abstract For some systems of nonlinear equationsF(x)=0 we derive an algorithm which iteratively constructs tight lower and upper bounds for the zeros ofF. The algorithm is based on a multisplitting of certain matrices thus showing a natural parallelism. We prove criteria for the convergence of the bounds towards the zeros and we investigate the speed of convergence.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02239746
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Some remarks on two interval-arithmetic modifications of the newton method (1992)
    Springer
    Computing 48 (1992), S. 125-128 
    Details
    ISSN: 1436-5057
    Keywords: 65H10 ; 65G10 ; Nonlinear equations ; systems of nonlinear equations ; interval Newton method ; interval Gaussian algorithm
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung In der vorliegenden Arbeit werden das Intervall-Newton-Verfahren und das vereinfachte Intervall-Newton-Verfahren betrachtet, um enge Schranken für die Lösungen nichtlinearer Gleichungssysteme zu erhalten. Unter starkem Bezug auf eine Arbeit von Alefeld über diese beiden Verfahren leiten wir einen Zusammenhang zwischen den beiden Matrizen her, die in der erwähnten Veröffentlichung bei der Formulierung hinreichender Konvergenzkriterien auftreten. Desweiteren beantworten wir eine dort gestellte Frage über den Abbruch der Verfahren nach endlich vielen Schritten.
    Notes: Abstract In this paper we consider the interval Newton method and its simplified version to find tight bounds for the solutions of systems of nonlinear equations. Referring to a paper of Alefeld on this subject, we derive a connection between the two matrices used there to formulate sufficient criteria for the convergence of these methods. We also answer an open question concerning the break down of the Newton method after a finite number of steps.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02241710
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Efficient methods for enclosing solutions of systems of nonlinear equations (1990)
    Springer
    Computing 44 (1990), S. 221-235 
    Details
    ISSN: 1436-5057
    Keywords: 65G10 ; 65H10 ; Newton's method ; Newton-Gauss-Seidel method ; nonlinear equations ; R-order ; interval analysis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Wir betrachten Modifikationen des Intervall-Newton-Verfahrens, welche zwei Ansätze miteinander verbinden: Mehrfache (z.B.s-fache) Verwendung derselben Auswertung der Jacobi-Matrix und näherungsweise Lösung der Newton-Gleichung mit einem „linearen” Iterationsprozeß. Insbesondere zeigen wir, daß dieR-Ordnung dieser Verfahrens+1 werden kann. Wir illustrieren unsere Ergebnisse an einem numerischen Beispiel.
    Notes: Abstract We consider modifications of the interval Newton method which combine two ideas: Reusing the same evaluation of the Jacobian several (says) times and approximately solving the Newton equation by some ‘linear’ iterative process. We show in particular that theR-order of these methods may becomes+1. We illustrate our results by a numerical example.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02262218
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    Numerical validation for an inverse matrix eigenvalue problem (1994)
    Springer
    Computing 53 (1994), S. 311-322 
    Details
    ISSN: 1436-5057
    Keywords: 65F15 ; 65G10 ; Inverse eigenvalue problem ; enclosure for the inverse eigenvalue problem ; interval computation ; Newton's method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Wir geben einen Algorithmus an, mit dem man Lösungen eines additiven inversen Matrizen-Eigenwertproblems nachweisen kann. Der Algorithmus beruht auf dem Newton-Verfahren, für das ein neues Abbruchkriterium verwendet wird. Er liefert enge Schranken für die Lösungen des Problems und garantiert so die meisten ihrer führenden Ziffern in einem gegebenem Gleitpunktsystem.
    Notes: Abstract We describe an algorithm with which one can verify solutions of an additive inverse matrix eigenvalue problem. The algorithm is based on Newton's method using a new criterion for terminating the iteration. In addition, it yields tight interval bounds for the solutions of the problem, thus guaranteeing most of their leading digits in a given floating point system.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02307382
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    Paper (German National Licenses)
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  • 5
    Electronic Resource
    Electronic Resource
    Micropuncture studies on the renal handling of 2,4-diamino-6,7-dimethylpteridine (1979)
    Springer
    Naunyn-Schmiedeberg's archives of pharmacology 306 (1979), S. 287-293 
    Details
    ISSN: 1432-1912
    Keywords: 2.4-diamino-6.7-dialkylpteridine ; Diuretics ; Micropuncture ; Tubular transport ; Rat kidney
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Summary The excretion of the diuretic substance DADMP (2.4-diamino-6.7-dimethylpteridine) and of DMP (6.7-dimethylpterin) was studied on single nephrons of the rat kidney using microperfusion and microinjection techniques. In the proximal tubule only DADMP was reabsorbed to a significant degree. Fractional reabsorption rate was independent of the load applied and the permeability constant was found to be 2.2·10−4 cm·s−1. Similar results were obtained in nephrons in which the substances, with inulin, were injected from middle proximal tubular puncture sites and recovered in the urine. DMP appeared in the urine quantitatively and simultaneously with the injected inulin. DADMP recovery, however, was only 20–30% of the injected load during the injection period and after 2 h some 70% was recovered from the urine of both kidneys. The reabsorbed fractions were independent of the loads applied, which varied between 2·10−13 mol·min−1 and 10−9 mol·min−1. A comparison of the microperfusion and the microinfusion data suggests that the reabsorption of DADMP occurs predominantly in the proximal convolution, and it appears that the differences between the renal handling of DMP and DADMP are explicable by their different lipid solubilities.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00507116
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    Paper (German National Licenses)
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