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  • AMS(MOS): Primary 65F05  (1)
  • CR: G.1.3  (1)
  • 1
    Electronic Resource
    Electronic Resource
    On the invariance of perturbed null vectors under column scaling (1984)
    Springer
    Numerische Mathematik 44 (1984), S. 61-65 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65F20 ; 65F35 ; CR: G.1.3
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary It is shown that the approximate null vector of a perturbed degenerate matrix behaves linearly under column scaling up to second order terms in the perturbation. This result has important consequences for an estimation technique known to numerical analysts as total least squares and to statisticians as latent root regression.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01389755
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    On a direct method for the solution of nearly uncoupled Markov chains (1991)
    Springer
    Numerische Mathematik 59 (1991), S. 1-11 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): Primary 65F05 ; 65G05 ; Secondary: 15A51
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary This note is concerned with the accuracy of the solution of nearly uncoupled Markov chains by a direct method based on the LU decomposition. It is shown that plain Gaussian elimination may fail in the presence of rounding errors. A modification of Gaussian elimination with diagonal pivoting and correction of small pivots is proposed and analyzed. It is shown that the accuracy of the solution is affected by two condition numbers associated with aggregation and the coupling respectively.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01385767
    Library Location Call Number Volume/Issue/Year Availability
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    Paper (German National Licenses)
    Fulltext
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