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  • ddc:000  (2)
  • 65F35  (1)
  • Mathematics Subject Classification (1991):65F15  (1)
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  • 1
    Digitale Medien
    Digitale Medien
    The product-product singular value decomposition of matrix triplets (1991)
    Springer
    BIT 31 (1991), S. 711-726 
    Details
    ISSN: 1572-9125
    Schlagwort(e): 65F25 ; 65F30 ; 65F35 ; singular value decomposition ; matrix product ; implicit Kogbetliantz technique
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract A new decomposition of a matrix triplet (A, B, C) corresponding to the singular value decomposition of the matrix productABC is developed in this paper, which will be termed theProduct-Product Singular Value Decomposition (PPSVD). An orthogonal variant of the decomposition which is more suitable for the purpose of numerical computation is also proposed. Some geometric and algebraic issues of the PPSVD, such as the variational and geometric interpretations, and uniqueness properties are discussed. A numerical algorithm for stably computing the PPSVD is given based on the implicit Kogbetliantz technique. A numerical example is outlined to demonstrate the accuracy of the proposed algorithm.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01933183
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  • 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
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  • 3
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    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
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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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