Geodesic
A new algorithm for the SVD of a long product of matrices and the stability of products
Electronic transactions on numerical analysis, Tome 5 (1997), pp. 29-47.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Lyapunov exponents can be estimated by accurately computing the singular values of long products of matrices, with perhaps 1000 or more factor matrices. These products have extremely large ratios between the largest and smallest eigenvalues. A variant of Rutishauser's Cholesky LR algorithm for computing eigenvalues of symmetric matrices is used to obtain a new algorithm for computing the singular values and vectors of long products of matrices with small backward error in the factor matrices. The basic product SVD algorithm can also be accelerated using hyperbolic Givens' rotations. The method is competitive with Jacobi-based methods for certain problems as numerical results indicate.
Classification : 65F15, 34D08
Keywords: SVD, products of matrices, Lyapunov exponents 
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     title = {A new algorithm for the {SVD} of a long product of matrices and the stability of products},
     journal = {Electronic transactions on numerical analysis},
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     url = {http://geodesic.mathdoc.fr/item/ETNA_1997__5__a3/}
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Stewart, David A. A new algorithm for the SVD of a long product of matrices and the stability of products. Electronic transactions on numerical analysis, Tome 5 (1997), pp. 29-47. http://geodesic.mathdoc.fr/item/ETNA_1997__5__a3/