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  • 1
    Electronic Resource
    Electronic Resource
    Precise domains of convergence for the block SSOR method associated withp-cyclic matrices (1989)
    Springer
    BIT 29 (1989), S. 311-320 
    Details
    ISSN: 1572-9125
    Keywords: AMS(MOS): 65F10 ; CR: 5.14
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We apply Rouché's theorem to the functional equation relating the eigenvalues of theblock symmetric successive overrelaxation (SSOR) matrix with those of the block Jacobi iteration matrix found by Varga, Niethammer, and Cai, in order to obtain precise domains of convergence for the block SSOR iteration method associated withp-cyclic matricesA, p≥3. The intersection of these domains, taken over all suchp's, is shown to coincide with the exact domain of convergence of thepoint SSOR iteration method associated withH-matricesA. The latter domain was essentially discovered by Neumaier and Varga, but was recently sharpened by Hadjidimos and Neumann.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01952685
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Convergent nonnegative matrices and iterative methods for consistent linear systems (1978)
    Springer
    Numerische Mathematik 31 (1978), S. 265-279 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65 F 10 ; CR: 5.14
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary In this paper we study linear stationary iterative methods with nonnegative iteration matrices for solving singular and consistent systems of linear equationsAx=b. The iteration matrices for the schemes are obtained via regular and weak regular splittings of the coefficients matrixA. In certain cases when only some necessary, but not sufficient, conditions for the convergence of the iterations schemes exist, we consider a transformation on the iteration matrices and obtain new iterative schemes which ensure convergence to a solution toAx=b. This transformation is parameter-dependent, and in the case where all the eigenvalues of the iteration matrix are real, we show how to choose this parameter so that the asymptotic convergence rate of the new schemes is optimal. Finally, some applications to the problem of computing the stationary distribution vector for a finite homogeneous ergodic Markov chain are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01397879
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    LU decompositions of generalized diagonally dominant matrices (1982)
    Springer
    Numerische Mathematik 40 (1982), S. 57-69 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65F05 ; CR: 5.14
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Using the simple vehicle ofM-matrices, the existence and stability ofLU decompositions of matricesA which can be scaled to diagonally dominant (possibly singular) matrices are investigated. Bounds on the growth factor for Gaussian elimination onA are derived. Motivation for this study is provided in part by applications to solving homogeneous systems of linear equationsAx=0, arising in Markov queuing networks, input-output models in economics and compartmental systems, whereA or −A is an irreducible, singularM-matrix. This paper extends earlier work by Funderlic and Plemmons and by Varga and Cai.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01459075
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    Paper (German National Licenses)
    Fulltext
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