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  • Lanczos algorithm  (1)
  • Numerical rank  (1)
  • Unstructured meshes  (1)
  • 1
    Digitale Medien
    Digitale Medien
    Transpose-free formulations of Lanczos-type methods for nonsymmetric linear systems (1998)
    Springer
    Numerical algorithms 17 (1998), S. 51-66 
    Details
    ISSN: 1572-9265
    Schlagwort(e): Lanczos algorithm ; quasi-minimal residual algorithm ; bi-conjugate gradients algorithm ; nonsymmetric linear systems ; Krylov subspace methods ; 65F10 ; 65N20
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract We present a transpose-free version of the nonsymmetric scaled Lanczos procedure. It generates the same tridiagonal matrix as the classical algorithm, using two matrix–vector products per iteration without accessing AT. We apply this algorithm to obtain a transpose-free version of the Quasi-minimal residual method of Freund and Nachtigal [15] (without look-ahead), which requires three matrix–vector products per iteration. We also present a related transpose-free version of the bi-conjugate gradients algorithm.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1023/A:1011637511962
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  • 2
    Digitale Medien
    Digitale Medien
    Additive Schwarz domain decomposition methods for elliptic problems on unstructured meshes (1994)
    Springer
    Numerical algorithms 8 (1994), S. 329-346 
    Details
    ISSN: 1572-9265
    Schlagwort(e): Unstructured meshes ; non-nested coarse meshes ; additive Schwarz algorithm ; optimal convergence rate ; 65N30 ; 65F10
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract We give several additive Schwarz domain decomposition methods for solving finite element problems which arise from the discretizations of elliptic problems on general unstructured meshes in two and three dimensions. Our theory requires no assumption (for the main results) on the substructures which constitute the whole domain, so each substructure can be of arbitrary shape and of different size. The global coarse mesh is allowed to be non-nested to the fine grid on which the discrete problem is to be solved and both the coarse meshes and the fine meshes need not be quasi-uniform. In this general setting, our algorithms have the same optimal convergence rate of the usual domain decomposition methods on structured meshes. The condition numbers of the preconditioned systems depend only on the (possibly small) overlap of the substructures and the size of the coares grid, but is independent of the sizes of the subdomains.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02142697
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  • 3
    Digitale Medien
    Digitale Medien
    Low-rank revealing QR factorizations (1994)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 1 (1994), S. 33-44 
    Details
    ISSN: 1070-5325
    Schlagwort(e): Rank revealing QR factorization ; Column pivoting ; Numerical rank ; Subset selection ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: Rank revealing factorizations are used extensively in signal processing in connection with, for example, linear prediction and signal subspace algorithms. We present an algorithm for computing rank revealing QR factorizations of low-rank matrices. The algorithm produces tight upper and lower bounds for all the largest singular values, thus making it particularly useful for treating rank deficient problems by means of subset selection, truncated QR, etc. The algorithm is similar in spirit to an algorithm suggested earlier by Chan for matrices with a small nullity, and it can also be considered as an extension of ordinary column pivoting.
    Zusätzliches Material: 1 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/nla.1680010105
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