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  • 1
    Electronic Resource
    Electronic Resource
    Optimal interval enclosing of certain sets of matrices, with application to monotone enclosing of square roots (1980)
    Springer
    Computing 25 (1980), S. 283-295 
    Details
    ISSN: 1436-5057
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung In dieser Arbeit werden zwei Halbordnungen für symmetrische Matrizen zueinander in Beziehung gesetzt, nämlich die durch den KegelK der elementweise nichtnegativen Matrizen definierte natürliche Halbordnung ≤ und die durch den KegelK D der nichtnegativ definiten Matrizen erzeugte definite Halbordnung $$ \leqslant \cdot$$ . Als Hauptresultat der Arbeit wird gezeigt, wie ein Matrixintervall im Sinne der definiten Halbordnung in optimale Schranken bezüglich der natürlichen Halbordnung eingeschlossen werden kann. Mit diesem Ergebnis ist es möglich, aus einer Lösungseinschließung mit der definite Halbordnung eine numerisch verwendbare Einschließung auf der Basis der natürlichen Halbordnung zu berechnen. Insbesondere kann auf diesem Wege ein stets und überdies quadratisch konvergentes Verfahren zur elementweisen monotonen Einschließung der Quadratwurzel einer symmetrischen, positiv definiten Matrix angegeben werden.
    Notes: Abstract In this paper, two kinds of partial ordering for symmetric matrices are related to each other, namely, the natural partial ordering ≤ generated by the coneK of elementwise nonnegative matrices, and the definite partial ordering $$ \leqslant \cdot$$ generated by the coneK D of nonnegative definite matrices. The main result of this paper shows how a matrix interval in the sense of the definite partial ordering can be enclosed between optimal bounds with respect to the natural partial ordering. By means of this result, it is possible to compute a numerically practicable inclusion based on the natural partial ordering from a given inclusion of some matrix with the definite partial ordering. In this way, an always and moreover quadratically convergent method of elementwise enclosing the square root of a positive definite, symmetric matrix can be constructed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02242005
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    On the R-order of coupled sequences II (1982)
    Springer
    Computing 29 (1982), S. 73-81 
    Details
    ISSN: 1436-5057
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Die Bestimmung der R-Ordnung τ von Folgen {x n, i ∼, die über ein System (3) von Ungleichungen miteinander verkoppelt sind, wird wie in der vorangegangenen Arbeit [3] auf die nichtnegative Lösbarkeit des Systems (4) von linearen Ungleichungen zurückgeführt. Weiterhin wird gezeigt, daß die beste R-Ordnung τ, welche sich aus (3) herleiten läßt, gleich dem Spektralradius einer bestimmten Matrix ist, welche aus in (3) auftretenden Exponenten gebildet wird.
    Notes: Abstract As in the preceding paper [3], the question whether some of the sequences {x n, i } coupled by a system (3) of inequalities converge at least with a certain R-order τ is reduced to the nonnegative solvability of the system (4) of linear inequalities. Further, the optimal R-order τ implied by (3) is characterized as the spectral radius of a certain matrix composed of exponents appearing in (3).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02254852
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  • 3
    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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  • 4
    Electronic Resource
    Electronic Resource
    Determination of the cone radius for positive concave operators (1984)
    Springer
    Computing 33 (1984), S. 37-49 
    Details
    ISSN: 1436-5057
    Keywords: 65H10 ; 90C30 ; 15A48 ; Iterative processes ; bestR-orders ; cone radius of concave operators ; spectral radii ; partial ordering
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Die Berechnung der bestenR-Ordnung von Folgen aus iterativen Näherungsverfahren führt auf die Ermittlung des hier eingeführten Kegelradius bestimmter konkaver Operatoren. Das Hauptergebnis der Arbeit ist die Darstellung des Kegelradius als Infimum der Spektralradien aller den konkaven Operator majorisierenden linearen Operatoren. Diese Charakterisierung ist von numerischem Intersse.
    Notes: Abstract The computation of bestR-orders of sequences produced by iterative methods leads to the determination of the cone radius of certain concave operators. The main result of the paper is the representation of the cone radius as the infimum of spectral radii of all linear operators majorizing the concave operator. This characterization is of numerical interest.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02243074
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  • 5
    Electronic Resource
    Electronic Resource
    Human body composition as related to surface area (1980)
    Springer
    European journal of pediatrics 135 (1980), S. 147-151 
    Details
    ISSN: 1432-1076
    Keywords: Body cell mass ; Body composition ; Body fat ; Energy metabolism ; Surface area ; Total body potassium
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Abstract There is a linear relationship between extracellular fluid and body surface area in man. During growth the body cell mass, fat-free solids, and body fat proportions of body weight increase while the extracellular fluid fraction decreases. Growth stops in men as soon as the body cell mass reaches 22.5 kg/m2 body surface area and in women when it reaches 16.9 kg/m2. The non-muscle cell mass and the muscle cell mass reach a 1:4 ratio in men whereas in women a 1:3.5 proportion—which is more favorable for pregnancy and lactation—is reached. The body composition of the newborn and the infant have fetal characteristics with a low body fat: surface area ratio and a low non-muscle cell mass: surface area ratio. The basal metabolic rate depends on the amount of non-muscle cell mass present, and the total energy change depends on body cell mass. This has been established by measurements of total body potassium, thiosulfate space, total body sodium, 24 h urine creatinine values and basal metabolic rate.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00441633
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    Paper (German National Licenses)
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