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|Title:||A QR-type reduction for computing the SVD of a general matrix product/quotient|
|Authors:||Chu, D. |
De Lathauwer, L.
De Moor, B.
|Source:||Chu, D., De Lathauwer, L., De Moor, B. (2003-07). A QR-type reduction for computing the SVD of a general matrix product/quotient. Numerische Mathematik 95 (1) : 101-121. ScholarBank@NUS Repository. https://doi.org/10.1007/s00211-002-0431-z|
|Abstract:||In this paper, a QR-type reduction technique is developed for the computation of the SVD of a general matrix product/quotient A = A1 s1 A2 s2 ⋯ Am sm with Ai ∈ Rn×n and si = 1 or si = -1. First the matrix A is reduced by at most m QR-factoizations to the form Q11 (1) (Q21 (1))-1, where Q11 (1), Q21 (1) ∈ Rn×n and (Q11 (1)T Q11 (1) + (Q21 (1))T Q21 (1) = I. Then the SVD of A is obtained by computing the CSD (Cosine-Sine Decomposition) of Q11 (1) and Q21 (1) using the Matlab command gsvd. The performance of the proposed method is verified by some numerical examples.|
|Source Title:||Numerische Mathematik|
|Appears in Collections:||Staff Publications|
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