Journal article
Exponential splittings of products of matrices and accurately computing singular values of long products
Linear algebra and its applications, Vol.309(1), pp.175-190
2000
DOI: 10.1016/S0024-3795(99)00273-6
Abstract
Accurately computing the singular values of long products of matrices is important for estimating Lyapunov exponents:
λ
i=
lim
n→∞(1/n)
logσ
i(A
n⋯A
1)
. Algorithms for computing singular values of products, in fact, compute the singular values of a perturbed product
(A
n+E
n)⋯(A
1+E
1)
. The question is how small are the relative errors of the singular values of the product with respect to these factorwise perturbations. In general, the relative errors in the singular values can be quite large. However, if the product has an exponential splitting, then the error in the singular values is
O(n
2
max
iκ
2(A
i)∥E
i∥
F)
, uniformly in
n. The
exponential splitting property is not directly comparable with the notion of hyperbolicity in dynamical systems, but is similar in philosophy.
Details
- Title: Subtitle
- Exponential splittings of products of matrices and accurately computing singular values of long products
- Creators
- Suely Oliveira - Department of Computer Science, University of Iowa, Iowa City, IA 52242-1419, USADavid E Stewart - Department of Mathematics, Room 14, McLean Hall, University of Iowa, Iowa City, IA 52242-1419, USA
- Resource Type
- Journal article
- Publication Details
- Linear algebra and its applications, Vol.309(1), pp.175-190
- DOI
- 10.1016/S0024-3795(99)00273-6
- ISSN
- 0024-3795
- eISSN
- 1873-1856
- Publisher
- Elsevier Inc
- Language
- English
- Date published
- 2000
- Academic Unit
- Computer Science; Mathematics
- Record Identifier
- 9984002450902771
Metrics
20 Record Views