The norm of a matrix after a similarity transformation

The norm of a similarity transformation of a matrix is studied considered as a function of the transformation matrix, and conditions for stationary points of this function are given in terms of properties of the transformed matrix.     

Complexity results for multicriterial and parametric network flows using a pathological graph of Zadeh

For two classes of network flow problems a worst-case analysis is given depending on the number of vertices of a pathological graph of Zadeh. Firstly, an exponential number of breakpoints in the optimal value function of the maximal flow problem in generalized networks with parametric capacities is demonstrated. Secondly, it is shown that the bicriterial min-cost flow has, in the worst case. an exponential number of efficient extreme point solutions in the objective space.

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Zusammenfassung Für zwei Klassen von Netzwerkflußproblemen wird eine worst-case Analyse in Abhängigkeit von der Anzahl der Knoten eines pathologischen Graphen von Zadeh vorgenommen. Demnach besitzt das Maximalflußproblem in verallgemeinerten Netzwerken mit parametrischen Kapazitätsbeschränkungen eine exponentielle Anzahl von Knickstellen in der Optimalwertfunktion. und kostenminimale Flüsse haben bereits für zwei Kriterien eine exponentielle Zahl von effizienten Eckpunkten im Bildbereich.

     

On the quadratic convergence of a generalization of the Jacobi Method to arbitrary matrices

A method of diagonalizing a general matrix is proved to be ultimately quadratically convergent for all normalizable matrices. The method is a slight modification of a method due to P. J. Eberlein, and it brings the general matrix into a normal one by a combination of unitary plane transformations and plane shears (non-unitary). The method is a generalization of the Jacobi Method: in the case of normal matrices it is equivalent to the method given by Goldstine and Horwitz.     

The method of conjugate gradients used in inverse iteration

An algorithm is devised that improves an eigenvector approximation corresponding to the largest (or smallest) eigenvalue of a large and sparse symmetric matrix. It solves the linear systems that arise in inverse iteration by means of the c-g algorithm. Stopping criteria are developed which ensure an accurate result, and in many cases give convergence after a small numer of c-g steps.     

Different methods for administering 17β-estradiol to ovariectomized rats result in opposite effects on ischemic brain damage

Background  

Numerous stroke studies have controversially shown estrogens to be either neuroprotective or neurodamaging. The discordant results observed in rat brain ischemia models may be a consequence of discrepancies in estrogen administration modes resulting in plasma concentration profiles far from those intended. To test this hypothesis we reproduced in detail and extended an earlier study from our lab using a different mode of 17β-estradiol administration; home-made silastic capsules instead of commercial slow-release 17β-estradiol pellets. Four groups of female rats (n = 12) were ovariectomized and administered 17β-estradiol or placebo via silastic capsules. All animals underwent MCAo fourteen days after ovariectomy and were sacrificed three days later.