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  • CR: G1.8  (1)
  • Schwarz Alternating Method  (1)
  • 1
    Digitale Medien
    Digitale Medien
    On block diagonal and Schur complement preconditioning (1990)
    Springer
    Numerische Mathematik 58 (1990), S. 79-93 
    Details
    ISSN: 0945-3245
    Schlagwort(e): AMS(MOS) ; 65N20 ; CR: G1.8
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary We study symmetric positive definite linear systems, with a 2-by-2 block matrix preconditioned by inverting directly one of the diagonal blocks and suitably preconditioning the other. Using an approximate version of Young's “Property A”, we show that the condition number of the Schur complement is smaller than the condition number obtained by the block-diagonal preconditioning. We also get bounds on both condition numbers from a strengthened Cauchy inequality. For systems arising from the finite element method, the bounds do not depend on the number of elements and can be obtained from element-by-element computations. The results are applied to thep-version finite element method, where the first block of variables consists of degrees of freedom of a low order.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01385611
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  • 2
    Digitale Medien
    Digitale Medien
    On the spectra of sums of orthogonal projections with applications to parallel computing (1991)
    Springer
    BIT 31 (1991), S. 76-88 
    Details
    ISSN: 1572-9125
    Schlagwort(e): 65N30 ; 65J10 ; 35J20 ; 15A18 ; Orthogonal Projections ; Parallel Computing ; Domain Decomposition ; Grid Refinement ; Schwarz Alternating Method
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract Many parallel iterative algorithms for solving symmetric, positive definite problems proceed by solving in each iteration, a number of independent systems on subspaces. The convergence of such methods is determined by the spectrum of the sums of orthogonal projections on those subspaces, while the convergence of a related sequential method is determined by the spectrum of the product of complementary projections. We study spectral properties of sums of orthogonal projections and in the case of two projections, characterize the spectrum of the sum completely in terms of the spectrum of the product.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01952785
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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