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  • 1
    Electronic Resource
    Electronic Resource
    On multilevel iterative methods for integral equations of the second kind and related problems (1985)
    Springer
    Numerische Mathematik 46 (1985), S. 147-157 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65J05 ; 65R20 ; CR: 61.9
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We describe a unifying framework for multigrid methods and projection-iterative methods for integral equations of the second kind, and for the iterative aggregation method for solving input-output relations. The methods are formulated as iterations combined with a defect correction in a subspace. Convergence proofs use contraction arguments and thus involve the nonlinear case automatically. Some new results are presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01400261
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    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
    Keywords: 65N30 ; 65J10 ; 35J20 ; 15A18 ; Orthogonal Projections ; Parallel Computing ; Domain Decomposition ; Grid Refinement ; Schwarz Alternating Method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01952785
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    Paper (German National Licenses)
    Fulltext
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