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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    BIT 36 (1996), S. 247-263 
    ISSN: 1572-9125
    Keywords: Block downdating ; Cholesky decomposition ; condition number ; error analysis ; perturbation theory ; seminormal equations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A new perturbation result is presented for the problem of block downdating a Cholesky decompositionX T X = R T R. Then, a condition number for block downdating is proposed and compared to other downdating condition numbers presented in literature recently. This new condition number is shown to give a tighter bound in many cases. Using the perturbation theory, an error analysis is presented for the block downdating algorithms based on the LINPACK downdating algorithm and stabilized hyperbolic transformations. An error analysis is also given for block downdating using Corrected Seminormal Equations (CSNE), and it is shown that for ill-conditioned downdates this method gives more accurate results than the algorithms based on the LINPACK downdating algorithm or hyperbolic transformations. We classify the problems for which the CSNE downdating method produces a downdated upper triangular matrix which is comparable in accuracy to the upper triangular factor obtained from the QR decomposition by Householder transformations on the data matrix with the row block deleted.
    Type of Medium: Electronic Resource
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  • 2
    ISSN: 1432-0533
    Keywords: Key words Reperfusion ; Cerebral blood flow ; Vascular smooth muscle cell ; Pericyte ; Scanning ; electron microscopy
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Abstract The present study was undertaken to ascertain the role of smooth muscles and pericytes in the microcirculation during hyperperfusion and hypoperfusion following ischemia in rats. Paired external carotids, the pterygopalatine branch of the internal carotids and the basilar artery were exposed and divided. Reversible inflatable occluders were placed around the common carotids. After 24 h, the unanesthetized rat underwent 10-min ischemia by inflating the occluders. Continuous cortical cerebral blood flow (c-CBF) was monitored by laser Doppler flowmetry. The measured c-CBF was below 20% of control (P 〈 0.001) during ischemia. A c-CBF of 227.5 ± 54.1% (P 〈 0.001) was obtained during reperfusion hyperemia. A c-CBF of 59.7 ± 8.8% (P 〈 0.001) occurred at the nadir of postischemic hypoperfusion, and this was followed by a second hyperemia. The cytoarchitecture of the vascular smooth muscles and pericytes was assessed by scanning electron microscopy. Samples were prepared using a KOH-collagenase digestion method. In control rats, arteriolar muscle cells showed smooth surfaces. Capillary pericytes were closely apposed to the endothelium. Immediately after reperfusion, transverse membrane creases were observed on the smooth muscle surfaces. During maximal hyperemia the creases disappeared. When c-CBF started to decrease the creases became visible again. Throughout the postischemic hypoperfusion the creases remained. Capillary endothelial walls became tortuous in the late phase of hypoperfusion. During the second hyperemia most arteriolar muscle cells showed smooth surfaces. Some pericytes appeared to have migrated from the vascular wall. The morphological changes of smooth muscle membranes suggest that they are related to specific perfusional disturbances during ischemia and reperfusion.
    Type of Medium: Electronic Resource
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