Volume 5, pp. 29-47, 1997.
A new algorithm for the SVD of a long product of matrices and the stability of products
David E. Stewart
Abstract
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.
Some properties of the product SVD factorization are also discussed,
including uniqueness and stability.
The concept of a
Full Text (PDF) [148 KB], BibTeX
Key words
SVD, products of matrices, Lyapunov exponents.
AMS subject classifications
65F15, 34D08.
Links to the cited ETNA articles
| [23] | Vol. 3 (1995), pp. 39-49 G. W. Stewart: On graded QR decompositions of products of matrices |
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