Geodesic
On graded QR decompositions of products of matrices
Electronic transactions on numerical analysis, Tome 3 (1995), pp. 39-49
This paper is concerned with the singular values and vectors of a product Mm = A1A2 $\cdot \cdot \cdot $Am of matrices of order n. The chief difficulty with computing them directly from Mm is that with increasing m the ratio of the small to the large singular values of Mm may fall below the rounding unit, so that the former are computed inaccurately. The solution proposed here is to compute recursively the factorization Mm = QRP T, where Q is orthogonal, R is a graded upper triangular, and P T is a permutation.
Classification : 65F30
Keywords: QR decomposition, singular value decomposition, graded matrix, matrix product 
@article{ETNA_1995__3__a7,
     author = {Stewart,  G.W.},
     title = {On graded {QR} decompositions of products of matrices},
     journal = {Electronic transactions on numerical analysis},
     pages = {39--49},
     year = {1995},
     volume = {3},
     zbl = {0855.65036},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_1995__3__a7/}
}
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Stewart,  G.W. On graded QR decompositions of products of matrices. Electronic transactions on numerical analysis, Tome 3 (1995), pp. 39-49. http://geodesic.mathdoc.fr/item/ETNA_1995__3__a7/