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  • AMS(MOS) 65F10  (1)
  • Hermitean matrix  (1)
  • Primary 15A42  (1)
  • 1
    Electronic Resource
    Electronic Resource
    Convergence properties of ART and SOR algorithms (1991)
    Springer
    Numerische Mathematik 59 (1991), S. 91-106 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS) 65F10 ; 15A06 ; CR: G1.3
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary ART algorithms with relaxation parameters are studied for general (consistent or inconsistent) linear algebraic systemsRx=f, and a general convergence theorem is formulated. The advantage of severe underrelaxation is reexamined and clarified. The relationship to solutions obtained by applying SOR methods to the equationRR T y=f is investigated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01385772
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    The limit of the spectral radius of block Toeplitz matrices with nonnegative entries (2000)
    Springer
    Integral equations and operator theory 36 (2000), S. 193-200 
    Details
    ISSN: 1420-8989
    Keywords: Primary 15A42 ; 15A48 ; 47B35 ; 47B65
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A bi-infinite sequence ...,t −2,t −1,t 0,t 1,t 2,... of nonnegativep×p matrices defines a sequence of block Toeplitz matricesT n =(t ik ),n=1,2,...,, wheret ik =t k−i ,i,k=1,...,n. Under certain irreducibility assumptions, we show that the limit of the spectral radius ofT n , asn tends to infinity, is given by inf{σ(ξ)∶ξ∈[0,∞]}, where σ(ξ) is the spectral radius of Σ j∈z t j ξ j .
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01202094
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    Paper (German National Licenses)
    Fulltext
  • 3
    Electronic Resource
    Electronic Resource
    On matrices that admit unitary reduction to band form (1998)
    Springer
    Mathematical notes 64 (1998), S. 753-760 
    Details
    ISSN: 1573-8876
    Keywords: Hermitean matrix ; unitary matrix ; band form of a matrix ; unitary reduction ; Krylov sequence ; Lanczos procedure
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract It is proved in the paper that any low rank perturbation of a Hermitian matrix is unitarily reducible to band form. Moreover, if a normal matrix is unitarily reducible to band form, then any of its rank one perturbations is unitarily reducible as well.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02313033
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    Paper (German National Licenses)
    Fulltext
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