Library

X
feed icon rss

Your email was sent successfully. Check your inbox.

An error occurred while sending the email. Please try again.

Proceed reservation?

Export
Filter
  • CR: G1.8  (1)
  • Schwarz Alternating Method  (1)
  • 1
    Electronic Resource
    Electronic Resource
    On block diagonal and Schur complement preconditioning (1990)
    Springer
    Numerische Mathematik 58 (1990), S. 79-93 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS) ; 65N20 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01385611
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 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
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
Close ⊗
This website uses cookies and the analysis tool Matomo. More information can be found here...