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  • Mathematics Subject Classification (1991):65F15  (1)
  • matrix product  (1)
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  • 1
    Electronic Resource
    Electronic Resource
    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
    Keywords: Mathematics Subject Classification (1991):65F15
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002110050175
    Library Location Call Number Volume/Issue/Year Availability
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    The product-product singular value decomposition of matrix triplets (1991)
    Springer
    BIT 31 (1991), S. 711-726 
    Details
    ISSN: 1572-9125
    Keywords: 65F25 ; 65F30 ; 65F35 ; singular value decomposition ; matrix product ; implicit Kogbetliantz technique
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01933183
    Library Location Call Number Volume/Issue/Year Availability
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    Paper (German National Licenses)
    Fulltext
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