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  • 1
    Electronic Resource
    Electronic Resource
    GMRESR: a family of nested GMRES methods (1994)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 1 (1994), S. 369-386 
    Details
    ISSN: 1070-5325
    Keywords: GMRES ; Unsymmetric linear systems ; Iterative solver ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Recently Eirola and Nevanlinna have proposed an iterative solution method for unsymmetric linear systems, in which the preconditioner is updated from step to step. Following their ideas we suggest variants of GMRES, in which a preconditioner is constructed per iteration step by a suitable approximation process, e.g., by GMRES itself. Our numerical experiments indicate that this may lead to considerable savings in CPU-time and memory requirements in typical CFD applications.
    Additional Material: 10 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nla.1680010404
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  • 2
    Electronic Resource
    Electronic Resource
    Approximate solutions and eigenvalue bounds from Krylov subspaces (1995)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 2 (1995), S. 115-133 
    Details
    ISSN: 1070-5325
    Keywords: Krylov subspace ; Lanczos process ; symmetric matrix ; conjugate gradients ; minimum residual ; Lehmann intervals ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Approximations to the solution of a large sparse symmetric system of equations are considered. The conjugate gradient and minimum residual approximations are studied without reference to their computation. Several different bases for the associated Krylov subspace are used, including the usual Lanczos basis. The zeros of the iteration polynomial for the minimum residual approximation (harmonic Ritz values) are characterized in several ways and, in addition, attractive convergence properties are established. The connection of these harmonic Ritz values to Lehmann's optimal intervals for eigenvalues of the original matrix appears to be new.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nla.1680020205
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