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  • 1995-1999  (2)
  • Chemistry  (1)
  • Gram-Schmidt downdating algorithm  (1)
  • 1
    Electronic Resource
    Electronic Resource
    Springer
    BIT 36 (1996), S. 166-181 
    ISSN: 1572-9125
    Keywords: QR decomposition downdating ; Gram-Schmidt downdating algorithm ; Householder transformation ; least squares problems ; modified Gram-Schmidt algorithm ; reorthogonalization
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A new algorithm for downdating a QR decomposition is presented. We show that, when the columns in the Q factor from the Modified Gram-Schmidt QR decomposition of a matrixX are exactly orthonormal, the Gram-Schmidt downdating algorithm for the QR decomposition ofX is equivalent to downdating the full Householder QR decomposition of the matrixX augmented by ann ×n zero matrix on top. Using this relation, we derive an algorithm that improves the Gram-Schmidt downdating algorithm when the columns in the Q factor are not orthonormal. Numerical test results show that the new algorithm produces far more accurate results than the Gram-Schmidt downdating algorithm for certain ill-conditioned problems.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Hoboken, NJ : Wiley-Blackwell
    Journal of Biomedical Materials Research 35 (1997), S. 249-254 
    ISSN: 0021-9304
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Medicine , Technology
    Notes: Osseous defects and fractures may require supplimentation to support and promote healing. Bioglass® (BG) may be a useful therapeutic for these conditions. Therefore, we executed a study to determine whether particulate BG could promote healing of 20-mm unilateral ostectomies in the radius of rabbits. Ostectomies were either treated with BG or remained untreated in the control (CTL) group. At 4 and 8 weeks post-treatment, ostectomies were assessed histomorphometrically and biomechanically. New bone formation was more intense contiguous to the host bone for both BG and CTL than centrally, yet BG animals displayed active mineralization throughout the ostectomy. The amount of bone within BG-filled defects was greater than CTLs at 4 weeks, whereas, at 8 weeks there was no difference. Biomechanically, the BG-treated limbs required more torque to break than did CTL limbs at 4 weeks; however differences were not significantly different. By 8 weeks, the BG-treated and CTLs, had comparable strength. Bioglass® may be a useful therapy to produce the early phase of osseous repair. However, improvements in handling properties of the particles will be needed to enhance efficacy. © 1997 John Wiley & Sons, Inc.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
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