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  • Articles  (4)
  • AMS(MOS): 65F10  (4)
  • Springer  (4)
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  • 2005-2009
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  • 1982  (4)
  • Mathematics  (4)
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  • Articles  (4)
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  • Springer  (4)
  • American Chemical Society
  • Annual Reviews
  • Blackwell Publishing Ltd
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  • 2005-2009
  • 1990-1994
  • 1980-1984  (4)
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  • Mathematics  (4)
  • 1
    Electronic Resource
    Electronic Resource
    On fixed point linear equations (1982)
    Springer
    Numerische Mathematik 38 (1982), S. 53-59 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65F10 ; 47B55 ; CR: 5.14
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary By means of successive partial substitutions it is possible to obtain new fixed point linear equations from old ones and it is interesting to determine how the spectral radius of the corresponding matrices varies. We prove that, when the original matrix is nonnegative, this variation is decreasing or increasing, depending on whether the original matrix has its spectral radius smaller or greater than 1. We answer in this way a question posed by F. Robert in [5].
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01395808
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    A modified bisection algorithm for the determination of the eigenvalues of a symmetric tridiagonal matrix (1982)
    Springer
    Numerische Mathematik 38 (1982), S. 417-419 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65F10 ; CR: 5.14
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary A modification to the well known bisection algorithm [1] when used to determine the eigenvalues of a real symmetric matrix is presented. In the new strategy the terms in the Sturm sequence are computed only as long as relevant information on the required eigenvalues is obtained. The resulting algorithm usingincomplete Sturm sequences can be shown to minimise the computational work required especially when only a few eigenvalues are required. The technique is also applicable to other computational methods which use the bisection process.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01396441
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  • 3
    Electronic Resource
    Electronic Resource
    On the convergence of the symmetric SOR method for matrices with red-black ordering (1982)
    Springer
    Numerische Mathematik 39 (1982), S. 113-117 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65F10 ; CR: 5.14
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We prove that if the matrixA has the structure which results from the so-called “red-black” ordering and ifA is anH-matrix then the symmetric SOR method (called the SSOR method) is convergent for 0〈ω〈2. In the special case thatA is even anM-matrix we show that the symmetric single-step method cannot be accelerated by the SSOR method. Symmetry of the matrixA is not assumed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01399315
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  • 4
    Electronic Resource
    Electronic Resource
    Zur Konvergenz eines Verfahrens von D.J. Evans zur iterativen Verbesserung einer Näherung für die inverse Matrix (1982)
    Springer
    Numerische Mathematik 39 (1982), S. 163-173 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65F10 ; CR: 5.14
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Recently D.J. Evans introduced an implicit matrix inversion process showing asymptotic behaviour which is superior to that of the well known Schulz-method. In this paper we give sufficient conditions for convergence, prove some error bounds and show that under certain conditions the iterates are converging monotonously.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01408691
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