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  • ddc:000  (2)
  • 65F20  (1)
  • Mathematics Subject Classification (1991):65F15  (1)
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  • 1
    Digitale Medien
    Digitale Medien
    ImplicitQR factorization of a product of three matrices (1991)
    Springer
    BIT 31 (1991), S. 375-379 
    Details
    ISSN: 1572-9125
    Schlagwort(e): 65F20 ; 65F25
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract We present a numerical algorithm for computing the implicit QR factorization of a product of three matrices, and we illustrate the technique by applying it to the generalized total least squares and the restricted total least squares problems. We also demonstrate how to take advantage of the block structures of the underlying matrices in order to reduce the computational work.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01931299
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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    Artikel (Nationallizenzen)
    Volltext
  • 2
    Digitale Medien
    Digitale Medien
    Computing the generalized singular values/vectors of large sparse or structured matrix pairs (1996)
    Springer
    Numerische Mathematik 72 (1996), S. 391-417 
    Details
    ISSN: 0945-3245
    Schlagwort(e): Mathematics Subject Classification (1991):65F15
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary. We present a numerical algorithm for computing a few extreme generalized singular values and corresponding vectors of a sparse or structured matrix pair $\{A,B\}$ . The algorithm is based on the CS decomposition and the Lanczos bidiagonalization process. At each iteration step of the Lanczos process, the solution to a linear least squares problem with $(A^{\rm T},B^{\rm T})^{\rm T}$ as the coefficient matrix is approximately computed, and this consists the only interface of the algorithm with the matrix pair $\{A,B\}$ . Numerical results are also given to demonstrate the feasibility and efficiency of the algorithm.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/s002110050175
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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    Artikel (Nationallizenzen)
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  • 3
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    Unbekannt
    A Numerical Algorithm for Computing the Restricted Singular Value Decomposition of Matrix Triplets. (1989)
    Details
    Publikationsdatum: 2014-02-26
    Beschreibung: This paper presents a numerical algorithm for computing the restricted singular value decomposition of matrix triplets (RSVD). It is shown that one can use unitary transformations to separate the regular part from a general matrix triplet. After preprocessing on the regular part, one obtains a matrix triplet consisting of three upper triangular matrices of the same dimensions. The RSVD of this special matrix triplet is computed using the implicit Kogbetliantz technique. The algorithm is well suited for parallel computation. {\bf Keywords:} Restricted singular values, matrix triplets, unitary transformations, implicit Kogbetliantz technique.
    Schlagwort(e): ddc:000
    Sprache: Englisch
    Materialart: reportzib , doc-type:preprint
    Format: application/pdf
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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    OPUS
  • 4
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    Restricted Singular Value Decomposition of Matrix Triplets. (1989)
    Details
    Publikationsdatum: 2014-02-26
    Beschreibung: In this paper we introduce the concept of restricted singular values (RSV's) of matrix triplets. A theorem concerning the RSV's of a general matrix triplet $ (A,B,C) $, where $ A \in C^{m\times n} $, $B\in C^{m\times p} $ and $ C\in C^{q\times n} $, which is called restricted singular value decomposition (RSVD) of matrix triplets, is derived. This result generalizes the wellknown SVD, GSVD and the recently proposed product induced SVD (PSVD). Connection of RSV's with the problem of determination of matrix rank under restricted perturbation is also discussed. {\bf Keywords:} Matrix rank, singular values, generalized singular values, product induced singular values, restricted singular values, matrix decompositions.
    Schlagwort(e): ddc:000
    Sprache: Englisch
    Materialart: reportzib , doc-type:preprint
    Format: application/pdf
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    OPUS
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