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  • 1985-1989  (2)
  • 1
    Electronic Resource
    Electronic Resource
    On the eigenvalue distribution of a class of preconditioning methods (1986)
    Springer
    Numerische Mathematik 48 (1986), S. 479-498 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65F10 ; CR: G1. 3
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary A class of preconditioning methods depending on a relaxation parameter is presented for the solution of large linear systems of equationAx=b, whereA is a symmetric positive definite matrix. The methods are based on an incomplete factorization of the matrixA and include both pointwise and blockwise factorization. We study the dependence of the rate of convergence of the preconditioned conjugate gradient method on the distribution of eigenvalues ofC −1 A, whereC is the preconditioning matrix. We also show graphic representations of the eigenvalues and present numerical tests of the methods.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01389447
    Library Location Call Number Volume/Issue/Year Availability
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    On the rate of convergence of the preconditioned conjugate gradient method (1986)
    Springer
    Numerische Mathematik 48 (1986), S. 499-523 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65F10 ; CR: G1.3
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We derive new estimates for the rate of convergence of the conjugate gradient method by utilizing isolated eigenvalues of parts of the spectrum. We present a new generalized version of an incomplete factorization method and compare the derived estimates of the number of iterations with the number actually found for some elliptic difference equations and for a similar problem with a model empirical distribution function.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01389448
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
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