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  • 1
    ISSN: 1436-5057
    Keywords: 65F10 ; 65G10 ; Interval arithmetic ; linear systems of equations ; iterative solution methods ; incompleteLU-decompositions ; comparison theorems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Vorgestellt wird eine Klasse von Iterationsverfahren zur Einschließung der Lösungsmenge durch einen Intervallvektor; dabei ist einen×n Intervall-H-Matrix und ein Intervallvektor. Der betrachtete Algorithmus verallgemeinert ein Iterationsverfahren von Meijerink/van der Vorst, das auf einer unvollständigenLU-Zerlegung einerM-MatrixA basiert. Es werden Aussagen über die Durchführbarkeit des Algorithmus, seiner Konvergenzgeschwindigkeit und seiner Einschließungsgüte gemacht. Da das ursprüngliche Verfahren von Meijerink/van der Vorst ein Spezialfall des vorliegenden Algorithmus ist, erhält man damit gleichzeitig seine Durchführbarkeit in der größeren Klasse derH-Matrizen. Als weitere Anwendung auf reelle Matrizen erhält man einen Zusammenhang zwischen demR 1-Faktor (Ortega/Rheinboldt [9]) des ursprünglichen Verfahrens und der zugrundeliegenden IndexmengeP.
    Notes: Abstract We present a class of iterative methods to enclose the solution set by an interval vector;A is varying in ann×n intervalH-Matrix andb is varying in an interval vector . The algorithm taken into consideration generalizes an iterative method of Meijerink/van der Vorst based on an incompleteLU-decomposition of anM-MatrixA. Theorems concerning the feasibility of the algorithm, its rate of convergence and its quality of enclosure are given. Since the original method of Meijerink/van der Vorst is a special case of our algorithm we have thus shown its applicability to the larger class ofH-matrices. Furthermore we relate theR 1-factor (as defined in Ortega/Rheinboldt [9]) of the original method to the underlying setP of indices.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Computing 49 (1992), S. 63-74 
    ISSN: 1436-5057
    Keywords: 65W05 ; 65F10 ; 65N20 ; Multisplittings ; parallel iterative methods ; SOR method ; local memory parallel computer
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Wir geben Konvergenz-und Vergleichsaussagen für parallele iterative Multisplitting-Verfahren mit verschiedenen Gewichtungsschemata. Insbesondere zeigen wir, daß bestimmte Gauss-Seidel Multisplitting-Verfahren nicht schneller konvergieren können als das gewöhnliche Gauss-Seidel-Verfahren. Wir berichten darüber hinaus über numerische Experimente auf einem 64-Prozessor-Rechner mit lokalem Speicher. Diese Experimente zeigen, daß der ‘naive’ Einsatz von Multisplittings leicht zu nicht zufriedenstellenden Ergebnissen führen kann, wenn mehr also nur ein paar Prozessoren eingesetzt werden.
    Notes: Abstract We present convergence and comparison theorems on parallel iterative multisplitting methods with different weighting schemes. In particular, we show that certain Gauss-Seidel multisplittings cannot converge faster than the usual Gauss-Seidel method. We also give numerical results on a 64 processor local memory computer. These experiments show that the ‘naive’ use of multisplittings can easily produce unsatisfactory results on parallel computers with more than just a few processors.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Pflügers Archiv 375 (1978), S. 9-16 
    ISSN: 1432-2013
    Keywords: Pterins ; Micropuncture ; Tubular transport ; Rat kidney
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Abstract In rat kidney, the rate of urinary biopterin [biopterin (B), 7,8-dihydrobiopterin (BH2), and 5,6,7,8-tetrahydrobiopterin (BH4)] excretion as measured by Crithidia assay, was found to be at least 3 times greater than the rate at which it is filtered (GFR·PBiopt.). At a renal blood flow of 6.43±1.34 ml/min per g kidney wt., biopterin concentrations in arterial and renal venous blood and plasma were similar [art. blood: 250±50 ng/ml, ren. venous blood: 247.3±50.9 ng/ml, art. plasma: 23.1±5.8 ng/ml, ren. venous plasma: 23.4±6.9 ng/ml (means±S.D.)]. 14C-BH4 and3H-inulin, infused by means of a micropump into late proximal segments of single nephrons at concentrations of 10−4–10−6 mol, were excreted at similar fractional rates (inulin: 0.85–0.97, BH4: 0.87–0.92, total recovery 1.00–1.09 and 0.99–1.11, respectively). Similar results were obtained with 6,7-dimethylpterin, but not with 6,7-dimethyl-5,6,7,8-tetrahydropterin. The latter is reabsorbed at a fractional rate of 0.20 at concentrations of 10−7 and 10−6 mol. In microperfusion studies in isolated proximal tubular segments in vivo et situ, no reabsorption of 6,7-dimethylpterin could be detected. In case of 6,7-dimethyl-5,6,7,8-tetrahydropterin (DMPH4) at concentrations of 5·10−5 and 10−5 mol/l, however, a permeability constant of 2.39·10−5 cm/s has been measured. From the fact that more biopterin leaves the kidney with urine plus venous blood than entered it is concluded that reduced biopterin is synthesized de novo in the kidney. With the exception of DMPH4, all types of biopterin are not significantly reabsorbed, but rather, are excreted into the urine due to an anisotropic permeability characteristic of the nephron.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Naunyn-Schmiedeberg's archives of pharmacology 306 (1979), S. 287-293 
    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
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